PreparationBake the Buttermilk Cake: 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. Make the Vanilla Syrup: 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. Make the Orange Cream-Cheese Frosting: 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. Assemble the cake: 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. Do Ahead 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.