Fill a medium sauce pan with 2 inches of oil. Place over medium-high heat. Line a large platter or baking sheet with paper towels to drain the fritters.
In a medium mixing bowl, stir together the flour, baking powder, pumpkin pie spice, and salt.
In a large mixing bowl, whisk together the eggs, pumpkin puree, sugar, and vanilla until well combined.
Add the flour mixture to the pumpkin mixture in two additions stirring with a spoon, until just combined, after each addition.
Use a small cookie scoop, or tablespoon measuring spoon, to portion the fritter batter into the hot oil. (I usually cook 3 to 4 fritters at a time.) Use a spider strainer (or a slotted spoon) to turn the fritters after 2 minutes. Cook for another 2-3 minutes until the fritters are golden brown on each side. Remove fritters from to oil to the paper towel-lined platter. Repeat with remaining batter.
Plate the fritter and using a sifter or a sieve, cover them with a generous dusting of powdered sugar. Serve immediately with cream cheese glaze for dipping
Notes
I really love nutmeg, but I would leave it out of the cream cheese glaze for this recipe.