Preheat oven to 350 degrees. Butter and flour a 9" x 13" cake pan.
In the bowl of a stand mixer with a paddle attachment, beat the butter until light and fluffy. Add in the sugar, and beat on medium for 1 minute. Scrape down the sides with a rubber spatula. Add in the vanilla bean paste, milk, and yogurt or sour cream. Mix for 30 seconds on medium speed until well incorporated. Add in the eggs, one at a time, and beat until well blended into the butter mixer.
With a fine sieve placed over the stand mixer bowl, sift together the baking powder, baking soda, salt, and flour.
Beat the flour into the butter mixture on low for 15 seconds. Scrape down the sides and beat until just combined. Turn the speed up to medium-high and beat the mixture for about 15 seconds. It should be light and fluffy. Do not over-mix.
Spoon the mixer into the prepared baking dish. Using an offset spatula, smooth the batter into the cake pan. Bake at 350 degrees for 25 minutes or until a cake tester comes out clean. Set on a wire rack to cool completely. Once completely cooled, top with my vanilla buttercream frosting.
Use a sharp knife and loosen the cake from the edges of the pan. Slice into squares and serve.