Preheat an oven to 375 degrees F (190 degrees C). Grease muffin pans or line with paper liners.
Whisk the flour, baking powder, and baking soda together in a bowl; set aside.
Beat the shortening and sugar together in a bowl until creamy. Beat in the eggs one at a time, followed by the sour cream and vanilla extract. Stir in the flour mixture until no dry lumps remain. Pour into the prepared muffin pans.
Bake in the preheated oven until golden and a toothpick inserted into the center comes out clean, 15 to 20 minutes. Cool completely on a wire rack before serving.