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Preheat oven to 350 degrees F. (For high altitude–375 degrees F.)
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Grease and flour two 8? or 9? round baking pans* and line with parchment or waxed paper.
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Whisk dry ingredients in a bowl and set aside.
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In the bowl of a stand mixer fitted with a paddle attachment, beat the shortening and sugar until very light and fluffy. Scrape down the sides and add the eggs one at a time, beating well and scraping the bowl down after each addition. Add the vanilla extract.
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Starting and ending with the dry ingredients, add the dry ingredients alternately with the milk. Only beat until combined. Remove bowl from mixer base and scrape the sides and bottom with a large silicone or rubber spatula to make sure all the ingredients are completely incorporated.
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Divide the batter evenly between the baking pans.
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Bake for 35-40 minutes, checking after 30 minutes. The tops will be lightly golden and springy to the touch. (Insert a cake tester into the center–only a few moist crumbs should cling to the tester.)
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Let cool for a few minutes in the pan, then remove to a wire rack to finish cooling.