Add in the 1 teaspoon sugar and the 2 packages of dry yeast. Let sit for 5 to 10 minutes until foamy.
Add in 1 cup of the flour, milk, egg, ⅓ cup granulated sugar, 2 tablespoons butter, and the pumpkin spice extract. Mix until thoroughly combined.
Add the remaining 2 ½ cups of flour. Stir until the dough forms a ball. Use your hands to knead in any remaining flour if necessary. The dough will be soft.
Grease a large bowl with 1 - 2 tablespoons of vegetable oil. Coat the dough with the oil and cover bowl with plastic wrap and allow the dough to rise in a warm area until doubled.
Punch down the dough and preheat the oven to 350 degrees. Spray your bundt pan with nonstick cooking spray.
Coating
In a small bowl, add the brown sugar, cinnamon, and pumpkin spice. Stir to combine.
Pinch dough balls about the size of walnuts from the punched down dough.
Dip each dough ball into the melted butter, then roll in the cinnamon and sugar mixture until well-coated.
Place dough balls evenly in the prepared bundt pan stacking on top of each other as needed.
Cover the pan with plastic wrap and let rise until doubled. This will take about 40 minutes.
Place in the preheated oven and bake for about 30 - 35 minutes or until golden brown.
Place a serving platter upside down on top of the hot monkey bread. Holding the platter and pan, immediately flip the pan so the platter is on the bottom to release the monkey bread. Allow the monkey bread to cool for 10 to 15 minutes.
Icing
Add the butter, cream cheese, and extract in a large bowl. Beat with a hand mixer on medium until smooth.
Add in 1 ½ cups of the powdered sugar and beat until incorporated.
For a thicker consistency, add the remaining powdered sugar. Icing should be a drizzle consistency. If the icing appears too stiff, you can add small amounts of milk until it reaches the desired consistency.
Drizzle on top of the warm monkey bread with a spoon.