Brown the Butter: Melt 1 cup of salted butter in a medium saucepan over medium heat. Swirl the pan as it bubbles and foams, watching for a deep amber color and nutty aroma, about 8-10 minutes. Cool for 10 minutes before using.

Mix Sugars: In a large bowl, combine cooled brown butter with 3/4 cup granulated sugar and 3/4 cup brown sugar. Whisk until smooth. Add 2 large eggs and 2 teaspoons vanilla, whisking until well blended.

Combine Dry Ingredients: In another bowl, whisk together 2 1/4 cups flour, 1 teaspoon baking powder, and 1/2 teaspoon baking soda. Gradually add to butter mixture, stirring until a soft dough forms.

Chill the Dough: Scoop the dough into balls and place on parchment-lined baking sheet. Cover and refrigerate for at least 30 minutes.

Bake the Cookies: Preheat oven to 350°F (175°C). Place dough balls on baking sheets, spaced 2 inches apart. Flatten slightly and bake for 8-10 minutes until edges are golden. Cool on a wire rack.

Prepare the Frosting: Beat together 1/2 cup softened butter until smooth. Gradually add 2 cups sifted powdered sugar, then incorporate 1 teaspoon vanilla extract, 1/2 teaspoon almond extract, and 2 tablespoons milk. Beat until smooth.

Frost the Cookies: Once cookies are cool, spread frosting on each using a knife or spatula. Add festive sprinkles if desired.