Position racks in the top and bottom third of the oven; preheat to 350°. Lightly spray three 9-inch nonstick cake pans with cooking spray. Sift the flour, cornstarch, baking powder, baking soda and salt into a large bowl. In a medium bowl, whisk the egg whites, egg and vanilla. In another large bowl, using an electric mixer, beat the butter until light and fluffy, about 2 minutes. Gradually add the sugar, occasionally stopping to scrape down the sides of the bowl, until well blended, about 2 minutes. Add the egg mixture in three additions, beating to blend after each addition. Beat in the flour mixture in three additions, alternating with the buttermilk in two additions, occasionally stopping to scrape down the sides of the bowl.
Divide the batter among the prepared cake pans. Bake until the cakes are puffed and a tester inserted into the centers comes out clean, 20 to 25 minutes. Let the cakes cool completely in the pans on wire racks. Invert onto the racks.
In a large bowl, using an electric mixer, beat the cream cheese, butter and vanilla until light and fluffy, about 3 minutes. Gradually beat in the confectioners’ sugar. Cover and refrigerate until firm enough to spread, 25 to 30 minutes.
Place 1 cake layer on a plate. Spread with 1/2 cup jam. Top with the second layer. Spread with the remaining 1/2 cup jam. Top with the third layer. Spread the frosting over the top and sides of the cake. Coat the sides of the cake with the nuts.
Note: If you’d rather make cupcakes, this batter makes enough for 24. Baking time will be about 15 minutes. Once the cupcakes cool, use a small knife to cut out a 1/2-inch hole in the top of each one. Fill with jam, frost and garnish with nuts.