Preheat the oven. Preheat the oven to 350°F (175°C) and line a muffin tin with paper liners.
Mix the wet ingredients. In a large mixing bowl, beat the shortening, sugar, egg, and vanilla with an electric mixer on medium speed until light and fluffy, about 2-3 minutes with a stand mixer or 4-5 minutes with a hand mixer.
Add the bananas. Add the mashed bananas to the bowl and mix at low speed until combined.
Combine the dry ingredients. Whisk together the flour, baking soda, and salt in a separate bowl.
Mix the wet and dry ingredients. Gradually add the dry ingredients to the wet ingredients, mixing until just incorporated.
Fill the muffin tin. Scoop the batter into the prepared muffin tin, filling each cup about 3/4 full.
Bake. Bake for 21-25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Cool the muffins. Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.