Preheat your oven to 350°F (175°C).
In a large mixing bowl, beat together the softened butter and sugar until light and fluffy (about 3-4 minutes).
Add the eggs, vanilla extract, and cake batter flavoring to the creamed mixture and beat until combined.
In another bowl, whisk together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Gently fold in the rainbow sprinkles to the cookie dough.
Using a cookie scoop, portion the dough onto a parchment-lined baking sheet.
Bake for 10-12 minutes or until the cookies are set and slightly golden around the edges.
Cool the cookies on the baking sheet for 5 minutes before transferring to a cooling rack.
While cooling, prepare the frosting by beating together the cream cheese and butter until smooth. Gradually add powdered sugar and milk until creamy.
Frost cooled cookies with the cream cheese frosting and top with additional sprinkles.