Preheat the oven to 160 C/320 F.
Grease and line three 6 inch round baking pans or 2 x 7-inch round baking pans.
Combine flour, baking powder, baking soda, and salt.
Cream butter and sugar until light and fluffy.
Add vanilla, followed by the eggs, one at a time.
Add the flour and sour cream alternating in three batches.
Lastly, add the brewed espresso.
Pour into the prepared baking pans.
Bake for 30 to 35 minutes until a skewer inserted comes clean.
Cool in the pan for 10 minutes then invert onto a cooling rack and cool completely before baking.