Preheat your oven to 350°F and grease a Bundt pan with butter or non-stick spray.
Cut the biscuit dough into quarters. In a bag, shake the granulated sugar, cinnamon, and pumpkin pie spice together.
Toss the dough pieces in the sugar-spice mix until well coated, then layer them into the Bundt pan.
In a small saucepan, melt the brown sugar, butter, canned pumpkin, and vanilla extract together over medium heat. Stir until well combined and pour over the biscuit pieces in the pan.
Bake for 40 minutes or until the bread is golden and cooked through. Let it cool for 5 minutes, then turn it out onto a serving plate.
For the icing, beat together cream cheese, powdered sugar, and milk until smooth. Drizzle over the warm monkey bread before serving.