01 - Heat 2 inches of vegetable oil in a heavy-bottomed pot or deep skillet to 350°F.
02 - Separate the biscuit dough into 8 rounds. Flatten each round slightly and make a hole in the center with a 1-inch cutter or bottle cap to form a donut shape.
03 - In a small bowl, mix the pumpkin purée and pumpkin pie spice. Spread a thin layer of the mixture between two biscuit rounds and press the edges to seal. Reshape and cut the center hole again if needed. Repeat with remaining biscuits to make filled donuts.
04 - Fry the donuts in batches for 1–2 minutes per side, or until golden brown and puffed. Remove with a slotted spoon and drain on paper towels.
05 - Mix the granulated sugar and cinnamon in a shallow bowl. While still warm, toss donuts in the cinnamon sugar to coat.
06 - For the glaze: Whisk powdered sugar, milk, vanilla, and pumpkin pie spice until smooth. Drizzle over cooled donuts if desired.