Preheat the oven to 350°F. Spray and line an 8 x 8-inch baking pan with parchment paper.
In a light-colored saucepan, melt butter over medium high heat. Wait for it to bubble, crackle and foam. It will quickly darken in color and become fragrant. Immediately pour into a heat safe bowl and let cool for 5 minutes.
Into the butter, add the sugars and whisk until mostly dissolved. Add the egg, egg yolk and continue to whisk until mixture is shiny and viscous, about a minute.
In a separate bowl, stir together flour, baking powder and salt. Add dry ingredients to the butter mixture along with the white chocolate chips and ¼ cup of sprinkles. Stir until combined.
Evenly spread mixture into prepared pan and sprinkle with remaining 2 tablespoons sprinkles. Bake for 25-28 minutes until the top is golden and the sides just begin to pull away from the pan. While warm, top generously with flaky sea salt if using. Let cool completely before slicing.
