01 - Pour 2 inches of vegetable oil into a heavy-bottomed pot or deep skillet. Heat the oil to 350°F, monitoring the temperature carefully with a kitchen thermometer.
02 - Separate the refrigerated biscuit dough into 8 individual rounds. Flatten each round gently with your palm, then use a 1-inch round cutter or bottle cap to cut a center hole, creating classic donut shapes.
03 - Combine the pumpkin purée and pumpkin pie spice in a small bowl, mixing until thoroughly incorporated. Spread a thin, even layer of the spiced pumpkin mixture between two biscuit rounds and press the edges firmly to seal completely. Reform the center hole if necessary during shaping.
04 - Carefully lower the filled donuts into the hot oil in batches, avoiding overcrowding the pan. Fry for 1 to 2 minutes per side until golden brown and puffed throughout. Transfer the cooked donuts using a slotted spoon and drain on layered paper towels.
05 - Whisk together the granulated sugar and ground cinnamon in a shallow bowl until evenly blended. While the donuts are still warm, coat each one thoroughly in the cinnamon sugar mixture, pressing gently to adhere the coating.
06 - Sift the powdered sugar into a medium bowl to remove lumps. Add the milk, vanilla extract, and pinch of pumpkin pie spice. Whisk vigorously until completely smooth and thickened to a pourable consistency. Drizzle generously over the cooled donuts.