Brown the butter by melting 1 stick unsalted butter in a medium saucepan over medium heat until it foams and turns golden brown with a nutty aroma, about 5-7 minutes. Remove from heat and let cool slightly.
Preheat the oven to 350°F (175°C) and line a cupcake pan with colorful liners.
In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In another bowl, combine the cooled brown butter, granulated sugar, and eggs (2 large eggs and 1 yolk). Mix until well combined. Add whole milk, sour cream, and boiling hot water, mixing until smooth.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Gently fold in the rainbow sprinkles. Do not overmix.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full. Bake for 18-20 minutes or until a toothpick inserted in the center comes out clean. Let cool in the pan for 5 minutes, then transfer to a cooling rack to cool completely.