Begin by preheating your oven to 350 degrees Fahrenheit. Lightly grease (with butter) AND line with parchment paper the bottoms of TWO 9-inch or 8-inch cake pans (for thicker layers) or THREE 6-inch cake pans.
In a bowl, whisk together the milk and lemon juice and set aside for 5-10 minutes until everything "activates" to create the dairy-free "buttermilk".
In a large bowl, whisk together the flour, baking powder, and salt until combined.
In a bowl, add the butter and sugar, beating them together using a hand-mixer (on high-speed), until pale and fluffy, about 2-3 minutes.
Add the eggs (one at a time) followed by the vanilla and yogurt, mixing until combined. On low-speed, add in the dry ingredients followed by the buttermilk and continue to mix until combined and the batter is smooth, about 3-4 minutes. NOTE: The batter should be thick, yet slowly run off the whisk once lifted.
Divide the batter evenly into each of the cake pans and bake for 30-35 minutes, or until a toothpick or butter knife comes out clean when tested in the centers.
Remove cakes from the oven and let them rest in the pan for 10 minutes or so before removing the cakes and placing them onto a cooling rack to fully cool. NOTE: Let them cool for at least 1-2 hours in a cool place.