Grease and line a 9x13 pan. Preheat the oven to 350°F.
In a stand mixer, beat together butter, sugar, and vanilla until light and fluffy (about 4-5 minutes).
Add eggs one at a time on low speed.
Mix in flour, baking powder, baking soda, and salt.
Pour in buttermilk while mixing on low until combined.
Fold in rainbow sprinkles with a spatula.
Pour batter into the prepared pan and bake for 30-35 minutes.
Allow the cake to cool completely.