Preheat oven to 350°F. Grease a 9x13-inch cake pan and line with parchment for easy removal.
Whisk dry ingredients: In a medium bowl, combine flour, baking powder, baking soda, and salt. Set aside.
Cream butter & sugar: In a large bowl using a hand or stand mixer, beat softened butter and sugar together until light and fluffy (about 2–3 minutes).
Add eggs & vanilla: Beat in eggs one at a time, scraping down the bowl as needed. Stir in vanilla.
Mix in sour cream and milk: Add sour cream and mix until smooth. Then add milk and mix again—don’t worry if it looks a little curdled at this point!
Add dry ingredients: Slowly mix in the dry ingredients on low speed until just combined. Do not overmix.
Fold in sprinkles: Gently fold in the sprinkles with a rubber spatula.
Bake: Pour the batter into the prepared pan and smooth the top. Bake for 32–36 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool completely in the pan.