Make the preserves first, since you’ll swirl some of it into the cake batter: purée the blueberries, with any juices they have exuded, in a blender or food processor. Pass the puré e through a coarse strainer or the medium disk of a food mill to remove the skins. In a heavy medium nonreactive saucepan, combine the blueberry purée with the sugar, lemon juice, lemon zest, and ginger. Bring to a gentle boil over medium heat, stirring frequently to dissolve the sugar. Continue cooking, stirring often, for 20 minutes, until the preserves have thickened and are reduced to 1 cup. To check for proper thickness, place 1 to 2 teaspoons on a small china or glass plate and put it in the freezer until cold. Drag your finger through the thickened purée: a clear path should remain. If it’s not ready, cook 5 minutes longer and repeat the test. Let the preserves cool, then cover and refrigerate for up to 5 days. Prepare the cake: preheat the oven to 350°F (175°C). Butter the bottom and sides of three 8-inch (20cm) round cake pans. Line the bottom of each pan with a round of parchment or waxed paper and butter the paper. In a mixer bowl, cream the butter, sugar, lemon zest, and lemon extract until light and fluffy. Gradually add the egg whites, 2 or 3 at a time, beating well between additions and stopping occasionally to scrape down the sides of the bowl. Combine the flour, baking powder, and salt; whisk gently to blend. In 2 or 3 alternating additions, beat the dry ingredients and milk into the butter mixture, scraping down the sides of the bowl several times. Beat on medium-high speed for about 1 minute to smooth out any lumps and aerate the batter. Scoop 1 cup of the batter into a small bowl. Divide the remainder equally among the 3 prepared cake pans, smoothing the tops with a rubber spatula. This gives you a “clean canvas” to work with. Add 2½ tablespoons of the Lemon-Blueberry Preserves to the reserved batter and blend well. Drizzle heaping teaspoons of this blueberry mixture over the batter in the pans. Using a skewer or paring knife, swirl the blueberry mixture in short strokes to drag it down through the lemon batter without mixing it in. Bake for about 25 minutes, or until a cake tester or wooden toothpick stuck into the center comes out clean and the cake begins to pull away from the sides of the pan. Let the layers cool in their pans for about 10 minutes, then turn out onto wire racks, carefully peel off the paper liners, and let cool completely, at least 1 hour. Make the frosting: in a small nonreactive saucepan, combine the sugar and water. Bring to a boil over medium heat, stirring to dissolve the sugar. Continue to boil without stirring, occasionally washing down the sides of the pan with a wet pastry brush, until the syrup reaches the soft-ball stage, 238°F (114°C) on a candy thermometer. Immediately remove from the heat. In a large mixer bowl, with an electric mixer on medium speed, beat the eggs briefly. Slowly add the hot syrup in a thin stream, pouring it down the sides of the bowl; be careful to avoid hitting the beaters, or the syrup may splatter. When all the syrup has been added, raise the speed to medium-high and beat until the mixture is very fluffy and cooled to body temperature. This can take 15 to 20 minutes. Reduce the mixer speed to medium-low and gradually add the softened butter, 2 to 3 tablespoons at a time, beating well between additions. As you’re adding the last few tablespoons of butter, the frosting will appear to break, then suddenly come together like whipped butter. Beat in the lemon juice, and the frosting is ready for use. To assemble the cake: place a cake layer, flat side up, on a cake stand or serving plate. Spread half of the Lemon-Blueberry Preserves over the top. Place a second layer on top of the first and spread the remaining preserves over it. Finally, place the third layer on top of the second and frost the sides and top of the cake with the lemon buttercream Frosting. Decorate with fresh blueberries.