Cream butter, oil, and sugar together until smooth and light. Stir in eggs and vanilla and whip until light and fluffy. Stir in dry ingredients slowly until all incorporated.
Refrigerate dough for 2-3 hours.
Preheat oven to 350. Line baking sheet with parchment paper and set aside.
Remove cookie dough from the refrigerator and roll it out on a lightly floured surface. You'll want the dough to be 1/4'-1/2' thick. Cut into shapes using cookie cutters and place 2 inches apart onto the prepared baking sheet.
Bake 7-9 minutes or until barely golden brown. Cool 5 minutes before removing to cooling rack.
For the frosting, stir butter, sugar, and vanilla together with the mixer on low. Slowly pour in milk until frosting starts to come together and becomes thick, light, and fluffy. {Go slow to make sure it stays on the thicker side!} Whip 1 minute.
Spread each cookie with a generous amount of frosting and top with a variety of sprinkles.