Vanilla-Buttermilk Sheet Cake With Raspberries and Orange Cream-Cheese Frosting

Place a rack in middle of oven; preheat to 350 °F. Flour a 13x9" pan, tapping out excess. Whisk baking powder, baking soda, salt, and remaining 2 cups flour in a medium bowl; set aside. Using an electric mixer on medium-high speed, beat butter and 1 1/2 cups granulated sugar in a large bowl, scraping down sides of bowl as needed, until light and creamy, about 5 minutes. Add egg yolks in 2 additions, scraping down bowl after each. Beat in vanilla. Reduce mixer speed to low, then add dry ingredients in 2 additions alternately with buttermilk in 2 additions, scraping down sides of bowl as needed. Using electric mixer on medium speed, beat egg whites in another large bowl until soft peaks form, 2 –3 minutes. Slowly add remaining 1/4 cup granulated sugar and continue to beat until stiff, glossy peaks form, about 3 minutes more. Fold half of the egg whites into flour mixture, then gently fold in remaining egg whites. Scrape batter into prepared pan; smooth surface. Bake, rotating pan halfway through and covering with foil during the last 15 minutes of baking, until golden brown, firm to the touch, and a tester inserted into the center comes out clean, 35 –40 minutes. Transfer pan to a wire rack and let cake cool.