To make the brown butter, melt butter in a clear heavy bottom pot. Once the butter starts to foam, whisk continuously until brown bits start to form. Remove from heat, pour into clean bowl, skim the foam from the top and cool to room temperature (25-30 minutes).
Line 8X8 baking pan with parchment paper and preheat oven to 350F. Whisk together flour, baking powder, baking soda and salt. Set aside.
In a stand mixer with paddle attachment, beat browned butter and sugar until smooth and well combined, about 3 minutes. Add eggs one at a time beating well after each one. Add vanilla extract, beating until well combined.
Add dry ingredients to the wet 1/2 batch at a time. By hand, mix each time until JUST combined. A few flour streaks is okay! Fold in sprinkles. Drop evenly sized scoops into the prepared pan. Evenly press batter/dough into the pan.
Bake at 350 for 25- 28 minutes. A toothpick inserted into the center should come out with a few moist crumbs. The edges will pull slightly from the pan. Cool in pan on a cooling rack for 30 minutes. Remove from the pan and cool an additional time as needed to room temperature before frosting.