Preheat oven to 300℉ and toast all-purpose flour on a baking sheet for 8 minutes. Let cool. Beat butter and sugar until light and fluffy. Mix in vanilla and milk, then fold in flour, salt, and sprinkles. Form discs of cookie dough, wrap in plastic, and freeze.

Preheat oven to 350℉ and prepare cake pans. In a medium bowl, sift flour, baking powder, and baking soda. Cream butter, sugar, and oil in a large bowl until pale. Add eggs, vanilla, and sour cream, then gradually mix in dry ingredients and buttermilk.

Divide batter among prepared pans and insert frozen cookie dough discs. Bake for 26-32 minutes. Cool cakes in pans for 10 minutes before transferring to wire racks.

For frosting, beat butter until creamy, then mix in softened cream cheese until fluffy. Gradually add powdered sugar, vanilla, and salt until smooth.

Trim domed tops of cooled cakes for even layers. Spread frosting on one layer, add cookie dough pieces, layer second cake, repeat, and add third layer. Apply a crumb coat and chill briefly.

Decorate with additional cookie dough balls and sprinkles. Slice and serve to delight your guests.