to 24 hours ahead of time: Brown the butter with the vanilla bean (see "Browning butter" in the Notes section, below ):
Run a paring knife down the center of the vanilla bean. Split it open with your fingers and use the knife to scrape out the tiny black seeds into a saucepan. Add the butter and the scraped vanilla bean and turn the heat to medium-high. (If you are using vanilla extract, brown the butter by itself.) Cook the butter with the vanilla bean and seeds until the butter caramelizes and emits a rich nutty vanilla aroma. Remove the vanilla bean, dry, and save for another use. Refrigerate the brown butter until it solidifies, 1 to 2 hours.
Preheat the oven to 350F and position the rack in the center of the oven. Grease and lightly flour two 9-inch cake pans or 16 muffin tins.
Cream the brown butter and add the eggs (see the Notes on creaming butter and room-temperature eggs ):
Place the chilled brown butter in the bowl of the stand mixer with the paddle attachment and beat on medium speed for 1 minute. Add the sugar and beat on medium-high speed. Toward the beginning of the creaming process the mixture will look dry and seem as though it will never come together. Continue creaming, stopping the mixer occasionally to scrape down the sides of the bowl, until the mixture becomes fluffy and almost beige in color, 8 to 12 minutes. Add the whole eggs and yolks, one at a time, and continue to beat until they are fully incorporated and the batter looks smooth and glossy, 1 to 2 minutes. Add the optional vanilla extract.
Assemble the dry ingredients.
In a dry bowl, whisk together all the dry ingredients.
Combine the flour and the milk:
With the mixer set on slow speed, add the dry ingredients to the butter in 3 parts, alternating with the milk. Once you have added the third portion, scrape down the sides of the bowl with a rubber spatula and briefly beat the batter on medium speed until just incorporated, 20 seconds.
Bake the cake:
Scrape the batter into the prepared cake pans, evening out the batter with a rubber spatula. Run a paring knife in a single circular motion through the batter, 1 inch from the edge of the pan. This will help the cake to rise evenly. Bake the cakes until the center is set and a tester inserted in the middle of the cake comes out clean, approximately 40 to 45 minutes. If you are making cupcakes, bake them for 30 minutes.
Allow the cake to cool on a wire rack for about 20 minutes. Run a paring knife around the edge of the pan and invert the cake onto a cooling rack. Allow the cake layers to cool to room temperature.
Fill and ice the cake:
If the individual cake layers domed a bit too much, use a long serrated knife to trim the peaked tops to even out the tops. Place the bottom layer on a decorative serving plate. Cut a 12-inch-long piece of wax paper into 4 equal strips. Place each strip under an edge of the cake to cover the rim of the plate, to prevent the plate from becoming coated with icing (see illustration). Smear a thin layer of icing over the bottom cake layer and then spread the raspberries evenly around on the buttercream. Using an offset spatula, gently smear a layer of buttercream over the raspberries, making sure to smear an equal amount of butter cream around the outer edge of the layer. Place the second cake layer on top. Evenly ice the whole cake with the remaining buttercream. Once you have smoothed out all the rough edges, remove the wax paper strips from underneath the cake to reveal a spotless serving platter.
Serving Suggestions:
Serve this cake the day it is made, at room temperature. Any icing will go with this cake, and any fruit or berry can be substituted as well. For an alternative cake filling, make one recipe of the buttercream for the outside of the cake and any of the mousse recipes as a filling. I also recommend the Milk Chocolate Frosting .
Storage: This cake will keep, covered and refrigerated, for 1 week. Allow it to come to room temperature before serving.
Browning butter:
Brown butter adds depth of flavor to all sorts of sauces and baked goods.
Brown butter is butter that is boiled until it reaches approximately 250F, at which point the milk proteins and sugar (lactose) brown through what are called maillard reactions, producing a complex, nutty, sweet flavor, with a caramel, hazelnut, brown sugar-like aroma.
There are several visual and aromatic clues to watch out for while you are browning butter. As the butter boils, a white foam will accumulate on the surface. In order to control the rate at which the butter browns, I recommend turning the heat down to medium when you see the foam forming.
Observe the butter very carefully. You will begin to notice brown freckles in the creamy white foam. It will then turn a universal beige-brown color and develop a nutty, butterscotch-like perfume. The boiled liquid butter under the foam will change color, from a clear yellow to a clear golden yellow. The best way to see this color change is by scooping up some of the butter with a dry ladle or spoon and then pouring the butter back into the pan, examining the color in the stream of hot butter. Once you have observed this color transformation and you have smelled the wonderful nutty aroma, remove the butter from the heat and set it aside.
If the butter continues to cook and brown further it takes on a golden brown color with an even stronger nutty caramelized flavor. (This deeply flavored butter is desirable for some recipes) If the butter is heated a bit more it takes on a solid brown color; it then loses its nutty sweetness and becomes somewhat acrid.
Also be aware that the browning milk solids, once caramelized, sink and collect at the bottom of the pan. When you pour off the brown butter you can strain the dark solids out; or, if desired, you can allow some to incorporate into your batter or sauce.
