Prepare your cake pans. Brush the bottoms and sides of your cake pans with melted butter. Line the bottoms and sides with parchment paper.
Combine the milk, oil, eggs, vanilla extract and vanilla bean paste in medium bowl. Whisk to thoroughly combine.
In the bowl of a stand mixer, combine the cake flour, sugar, baking powder, and salt. On low speed, mix for 1 minute.
With the mixer still running, add in the softened butter pieces, one or two pieces at a time. Mix until the mixture resembles cornmeal. You should be able to gather a bit in your hand, squeeze and you have a solid piece. This means the butter is evenly distributed.
With the mixer still on low, pour in a small amount of the liquid ingredients (about 1/2 cup) and mix until the flour mixture is moistened.
Turn the mixer speed to medium (4 or 6) and beat for *two full* minutes. The mixture should be whipped up, thick, and lighter in color.
Scrape the sides and bottom of the bowl to ensure everything is properly mixed.
With the mixer speed on low, add the remaining wet ingredients in three parts, scraping down the bowl after each addition has been mixed in.
Once all the wet ingredients have been incorporated, give the bowl a final scrape and mix with a spatula.
Evenly divide the batter among the prepared pans.
Bake the layers for 35-45 minutes. Check the cake at 30-35 minutes to test for doneness. If a toothpick comes out clean, and the top of the cake feels springy and set when touched, take the cakes out.
Tap the cake once, firmly against the counter to remove excess steam. If your cakes dome at all, use a clean kitchen towel to gently push the domes down. Cool the cakes for 15 minutes in the pans.
Run a palette or butter knife around the cakes in their pans before turning them out to cool completely on cooling racks.
Wrap in plastic wrap and chill in the refrigerator a couple hours.