Peach Upside-Down Cake

Place oven rack in lowest position; heat oven to 350 degrees F. Topping: Melt butter in a 9- or 10-inch cast-iron skillet; brush butter up sides of skillet to coat. Add sugars, crumbling brown sugar; cook, stirring over medium heat, until mixture bubbles and looks creamy and smooth, 2 to 3 minutes. Remove skillet from heat; arrange peach slices on top of butter mixture in concentric circles. Cake: Mix flour, baking powder, cinnamon, nutmeg, and salt in a medium bowl until blended. In a large bowl with a mixer on medium speed, beat butter and sugar until pale and fluffy, about 3 minutes; beat in eggs, 1 at a time, until blended. On low speed, beat in half of the flour mixture, milk, extracts, then the remaining flour mixture until batter is smooth. Spoon batter into skillet, and using a spatula, gently spread batter over peaches in an even layer to reach the sides of the skillet. Bake 35 to 40 minutes, until top is golden brown and a pick inserted in center comes out clean. Let cool in skillet on a rack 10 minutes. Run a knife around edge. Invert a serving plate over top of skillet. Using oven mitts, invert cake onto platter (replace any peach slices that stick to skillet). Serve warm or at room temperature, with whipped cream, if desired.