Preheat oven to 350 degrees. Butter an 8-by-12-inch cake pan, and line with parchment paper. Butter parchment; set aside. Sift flour, baking soda, baking powder, and salt into a medium bowl; set aside.
Put butter and 3/4 cup sugar into the bowl of an electric mixer fitted with the paddle attachment; mix on medium-high speed until pale and fluffy, about 4 minutes. Mix in egg yolks. Reduce speed to low. Add flour mixture in 3 batches, alternating with the buttermilk. Transfer batter to a medium bowl; set aside.
Put egg whites into the clean bowl of mixer fitted with the whisk attachment; beat on medium-high speed until foamy. Gradually add remaining 1/3 cup sugar, beating until soft peaks form. Gently fold half of egg-white mixture into batter with a rubber spatula. Fold in remaining egg-white mixture. Transfer to prepared pan.
Bake until light golden and a cake tester inserted into center comes out clean, 20 to 25 minutes. Let cool a wire rack 15 minutes. Invert onto rack; remove parchment. Let cool completely. Trim cake to 10 by 5 inches. Cake can be refrigerated, wrapped in plastic, up to 1 day.
Coat a 10-by-5-inch loaf pan with cooking cooking spray; line with parchment, allowing a 1-inch overhang on long sides. Coat parchment with cooking spray. Line with plastic wrap, allowing a 3-inch overhang.
Stir ice cream and peaches in a medium bowl; spread into prepared pan. Freeze until firm, about 2 hours. Spread 1 pint sorbet over ice cream; freeze until firm, about 1 hour. Spread with remaining pint sorbet; top with cake. Cover with plastic overhang. Freeze until firm, at least 2 hours or up to 4 days. To loosen cake from pan, wrap a damp, hot towel around pan. Lift out. Serve immediately.