Peaches-and-Cream Ice Cream Cake

INGREDIENTS

• 1/2 cup (1 stick) unsalted butter, softened, plus more for pan
• 1 1/2 cups cake flour (not self-rising)
• 1/2 teaspoon baking soda
• 1/4 teaspoon baking powder
• 1/4 teaspoon salt
• 1 cup sugar
• 2 large eggs, separated
• 1/2 cup buttermilk
• Vegetable-oil cooking spray
• 1 1/2 pints vanilla ice cream, slightly softened
• 1 1/2 pounds ripe peaches, cut into 1/2-inch pieces (about 2 1/4 cups)
• 2 pints peach sorbet, slightly softened