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.

Combine granulated sugar and 1/4 cup water in a medium saucepan. Scrape in vanilla seeds, add pod, and stir to combine. Bring to a boil, cover, and steep at least 15 minutes. Set aside to cool. Discard pod before using.

Using electric mixer on medium-high speed, beat cream cheese and butter in a large bowl until smooth, about 1 minute. Beat in orange zest, orange juice, and vanilla. Reduce mixer speed to low and beat in powdered sugar, scraping down bowl as needed, until light and fluffy, 2–3 minutes.

Using a pastry brush, brush top of cooled cake with 2 Tbsp. vanilla syrup; reserve remaining syrup for another use. Spread frosting over top of cake, swirling decoratively. Top with raspberries and edible flowers, if using.

Cake can be made 3 days ahead; wrap tightly in plastic and chill, or freeze up to 2 weeks. Syrup can be made 5 days ahead; store in an airtight container and chill. Frosting can be made 3 days ahead; cover with plastic wrap, pressing directly on surface, and chill. Bring to room temperature before using.