Preheat the oven to 350 degrees. Line a muffin tin with cupcake liners.

In a large bowl whisk together the sweet potato puree, milk, vanilla, vinegar, and vegetable oil. Set aside for 5 minutes.

In a medium bowl combine the flour, sugar, salt, baking powder, baking soda, cinnamon, and allspice.

Pour the dry ingredients into the wet ingredients and mix until a thick batter forms.

Using a large cookie scoop, scoop the batter into the prepared muffin tin.

Bake for 20 minutes. Remove from the oven and then transfer to a wire cooling rack to cool completely.

To make the frosting place the marshmallows in a microwave safe bowl. Heat for 15 seconds, remove and stir. Heat for another 15 seconds, remove and stir. Do this until the marshmallows are completely melted.

Place the melted marshmallows and butter in a large bowl and use a hand mixer on medium speed to blend together. Add in the powdered sugar, vanilla, and milk and beat until smooth. You may need to add additional milk to reach desired consistency.

Pipe the frosting onto the cupcakes.