Put 18 liners in tins or grease with butter or oil . Preheat oven to 350°.
Batter may be mixed by hand, with an electric mixer, or a standing mixer.
Put eggs in a large bowl and beat. Add pumpkin and blend in. Add all other ingredients and mix well. Taste for sweetness and add more xylitol as necessary.
Divide batter evenly between 18 cupcake cups. Batter should come just to the top of the tin but under the top of the paper liner.
Bake for 20-25 minutes or until cupcakes feel a little firm to the touch and a toothpick inserted in the center comes out clean. Cool completely before frosting.
Make the Frosting:
While the cupcakes are baking, make the frosting.
Put all ingredients in a medium bowl or the bowl of a standing mixer. Beat with an electric mixer or standing mixer until fully combined and light and fluffy. Frosting should be spreadable but not so warm that it starts to melt. Refrigerate covered, if necessary, until ready to use. May need to let stand for a few minutes after removing from the refrigerator to soften a little.
Top cupcakes with frosting. Keep refrigerated until ready to serve.
Recipe by Preheat to 350˚ at https://preheatto350.com/pumpkin-cupcakes-low-carb-gluten-free-sugar-free/