Preheat oven to 400F and line a baking sheet with parchment paper. Set aside.
In a mixing bowl, whisk together Bisquick, sugar, and pumpkin pie spice.
Add pumpkin puree, milk, egg, and oil. Stir together just until well-combined.
Using a large cookie scoop, scoop the batter out into 12 portions on the prepared baking sheet.
In a small bowl, prepare the sugar topping by stirring together the sugar and pumpkin pie spice. Sprinkle this mixture over the top of the rounds of batter.
Bake in preheated oven for about 11-13 minutes, until cooked through.
While the fritters are baking, prepare the glaze by whisking together the powdered sugar, pumpkin pie spice, vanilla extract, and milk in a small bowl.
Remove fritters from oven and turn on the broiler. Using a pastry brush, brush glaze over the top of each of the fritters.
Return the pan to the oven and broil for about 1 minute. The glaze will start to bubble up. Just keep a close eye on it so it doesn't burn!
Remove from oven and let cool for one or two minutes. Then brush the remaining glaze over the tops of the fritters. The glaze will harden to a satiny finish as it cools.
Enjoy warm or allow to cool completely.