Preheat oven to 350° F. Prepare three 6-inch cake pans by greasing and flouring the insides. If your pans tend to stick, cut out circles of parchment paper to line the bottoms.
In a stand mixer with a beater attachment, cream together the butter and sugar on medium until light in color and fluffy, about three minutes.
Add one egg at a time, mixing until fully incorporated after each addition.
In a medium-sized bowl, whisk together the flour, baking powder, baking soda, spices, and salt.
In a measuring cup, mix together the milk, sour cream, applesauce, and vanilla.
Set mixer to low. Add one-third of the flour mixture into the egg mixture. After it fully incorporates, pour in one-third of the liquid mixture. After the liquid fully incorporates, repeat the process until everything has been combined, ensuring to end with the flour.
Do not over-mix. Turn the mixer off the moment the last bits of flour disappear.
Remove bowl from mixer and run a rubber spatula around the bottom to make sure everything has been incorporated.
Divide batter into prepared pans. If you have a digital scale, weigh each pan to confirm you are doling out evenly.
Bake the cakes for about 30 minutes on the center rack. A cake tester should come out clean from the center and the cake tops should bounce back when lightly pressed.
Let the cakes cool in their pans for a few minutes before running a knife around the edges and carefully turning out onto a cooling rack.