To a medium bowl, add mashed sweet potatoes. Stir in the light brown sugar, cinnamon, and nutmeg until fully combined. Set aside.
On a lightly floured surface, roll out the pie crust to ⅛-inch thick. Use a 4-5 inch round cookie cutter to cut the crust. (You should get 26-28 pie crust rounds if using homemade; it may be less if using store-bought.)
Add 1 tablespoon of sweet potato filling to each round.
Fold each mini pie crust into a half-moon shape. Use water to wet the edges to help seal each crust. Crimp with a fork and set aside.
In a medium pot over medium heat, add 2-3 inches of oil. Heat the oil until it reaches a temperature of 375°F.*
Place 2-3 hand pies into the hot oil. Fry until golden brown (2-3 minutes). Transfer to a paper towel-lined baking sheet. (Before adding each batch of hand pies, make sure the temperature of the oil is at 375°F; it may cool down after each batch.)
In a small bowl, whisk together the confectioners' sugar and 6 tablespoons of milk. Add more milk if needed, 1 tablespoon at a time, until the glaze reaches a pourable consistency.
While the hand pies are still warm, coat each with the glaze.