Preheat oven to 350 degrees F. Lightly grease the bottom of two 9" round cake pans with cooking spray. Add a parchment paper round to the bottom of the pans, then spray the pans and the sides of the pans once more with cooking spray; set aside.
In a large bowl of a stand mixer, cream together the butter, oil, and sugar on medium-low speed until creamy and smooth, about 1-2 minutes. Add in the eggs, one at a time, beating well after each addition, followed by the vanilla extract and paste, if using. Scrape down the bottom and sides of the bowl if needed.
In a medium bowl, whisk together the flour, baking powder, and salt. Gradually add in the flour mixture to the cake batter, mixing well after each addition while alternating with the buttermilk. Alternate adding in the flour and buttermilk until a smooth cake batter comes together.
Divide the cake batter evenly among the two cake pans. Bake for approximately 25-30 minutes or until a toothpick or cake tester comes out clean or with moist but not wet crumbs. Cool the cakes on wire racks completely before frosting.
For the frosting: in the bowl of a stand mixer, cream together the butter and vanilla extract until smooth. Gradually add in the confectioners' sugar, about one cup at a time, alternating with some of the heavy cream until the frosting is light and fluffy.
Frost the cakes with your vanilla buttercream and garnish with sprinkles, if desired. For best results, store cake covered airtight at room temperature or in the fridge.
NOTE: For a 9x13 rectangular cake pan, bake for approximately 30-35 minutes. For cupcakes, bake for approximately 15-18 minutes. For three layers, bake for approximately 20-25 minutes.