Add about 2 inches of vegetable oil to a sauce pan and heat-up over medium heat. Place a few sheets of paper towels on a large plate or baking sheet to drain excess oil from fritters.
In a mixing bowl, combine the flour, baking powder, cinnamon, nutmeg, and salt.
Using a larger bowl, add the pumpkin puree, milk, egg, brown sugar, and vanilla. Using a whisk or an electric hand mixer, whisk the mixture until it is thoroughly combined.
Begin adding the flour mixture, half at a time, into the pumpkin mixture. Stir it together until it is fully combined. Batter should be on the thick side.
Use a tablespoon, or a small cookie scoop to add the fritter mixture to the hot oil. Do not overcrowd the pan, depending on the size, add 3-4 fritters at a time.
Cook fritter for 2-3 minutes and use a slatted spoon to gently turn it over. Cook an additional 3 minutes, or until they are golden brown. Remove them from the oil and place them on the paper towels to drain excess oil.
For the Glaze
While fritters are frying, use a medium size bowl and add all ingredients, excluding the milk.
Using a hand mixer or whisk, mix the glaze until it is thoroughly combined.
If the glaze is too thick, slowly whisk in a teaspoon of milk at a time- until desired consistency is achieved.
If you have any leftover (because they are that good), you can easily reheat them in the oven. Simply place them on a baking sheet and heat them in the oven on low-broil mode for 3-5 minutes.