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Combine flour, baking soda, pumpkin pie spice and salt in large mixing bowl. Set aside.
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Beat the eggs and sugar in mixing bowl. Add the pumpkin and oil (and applesauce if substituting) and mix well.
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Stir into the flour mixture just until moistened.
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Fold in chopped cranberries. (I left the small cranberries whole and the big cranberries I chopped in half.)
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Fill paper-lined muffin cups three-fourths full.
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Bake at 400 degrees F for 18-22 minutes or until a toothpick inserted in center comes out clean.
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Cool for 5 minutes in pans then remove to wire racks.