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Preheat oven to 400 degrees. Spray muffin tins or line with paper muffin cups.
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Whisk the flour, baking soda, salt, and cinnamon in a bowl until uniform. Set aside.
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In a large bowl, cream the butter and sugar with a wooden spoon until smooth, about 2 minutes. Add eggs, one at a time, mixing until well incorporated.
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Peel and mash bananas, and add them to the butter mixture using a potato masher (or a fork.) Stir in the milk or half-and-half, vanilla, and vinegar until the mixture is smooth and creamy. Add the prepared flour mixture, and stir until moistened.
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Fill muffin tins three-quarters full. BAKE 18 minutes, or until pale brown with rounded nubbly tops. Let cool on a wire rack for about 19 minutes before removing and serving.