01 - Preheat oven to 350°F. Line a 9x13 inch baking pan with parchment paper and lightly grease the surface.
02 - In a large mixing bowl, beat together unsalted butter and granulated sugar with an electric mixer on medium speed until the mixture is light and fluffy, about 2 to 3 minutes.
03 - Add eggs, one at a time, beating well after each addition. Stir in pure vanilla extract.
04 - In a separate bowl, whisk together all-purpose flour, baking powder, and salt until evenly mixed.
05 - Gradually add the dry ingredients into the creamed mixture, mixing just until a smooth dough forms.
06 - Transfer dough to the prepared baking pan. Spread evenly and smooth the surface with a spatula.
07 - Bake in preheated oven for 18 to 22 minutes, until edges are lightly golden and center is set. Do not overbake.
08 - Allow the bars to cool completely in the pan on a wire rack before frosting.
09 - In a clean bowl, beat softened butter until creamy. Gradually mix in powdered sugar, then add pure vanilla extract and heavy cream or milk. Beat on high speed for about 2 minutes until light and fluffy.
10 - Divide frosting evenly among three bowls. Leave one portion plain for white, tint one portion red using gel food coloring, and the third portion blue. Mix well to achieve even coloring.
11 - Dollop spoonfuls of each color frosting over the cooled bars. Swirl gently with an offset spatula for a marbled effect or spread in sections for stripes.
12 - Immediately garnish the surface with red, white, and blue sprinkles while the frosting is still soft.
13 - Carefully remove from the pan, cut into 24 even bars, and serve.