In the bowl of an electric mixer, beat the butter on medium speed until it is noticeably lighter in color. Add the sugar and continue beating until the grittiness is gone and the mixture is fluffy.
Add the eggs one at a time, breaking them first into a cup. Beat each egg completely into the butter-sugar mixture before adding the next one. After two eggs, stop the mixer and scrape down the sides of the bowl with a rubber spatula.
Sift the flour, baking powder, and salt into a bowl. Add about a fourth of it to the mix.
Mix the extracts into the milk, and add about a third of the milk to the mixing bowl. Alternate another quarter of the flour with another third of the milk, waiting until each addition has been completely blended before the next one. Scrape down the sides of the bowl after the last flour addition, and mix until completely smooth.
Coat the insides of three round nine-inch cake pans liberally with shortening and then add about a tablespoon of flour to each. Shake the flour around to coat completely, then pound the excess out.
Divide the batter among the pans. Bang the filled pans down on the counter to even out the batter. Bake for 25 minutes in the preheated 350-degree oven. Avoid opening the oven during the baking. After 25 minutes, check the the cakes. If they're browned at all, test them with a skewer. If it comes out clean, they're done.
Let the cakes cook in their pans for 10-15 minutes. Then turn them out onto cooling racks to complete cooling. (If they don't come right out, bang on the bottom of the pan a little.)
