Begin by warming the milk in a microwave or saucepan until it’s lukewarm. In a small bowl, combine the warmed milk and the active dry yeast. Gently stir and let it sit for about 5 minutes until it becomes frothy.
In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, brown sugar, salt, ground cinnamon, ground nutmeg, and ground ginger until well mixed.
Next, add the pumpkin puree, melted butter, egg, and the frothy yeast mixture to the bowl of dry ingredients. Using a wooden spoon or spatula, stir until a sticky dough forms.
Transfer the dough onto a lightly floured surface and knead it for about 5-7 minutes, adding a little flour as necessary, until the dough is smooth and elastic. Place the dough into a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm, draft-free area for 1 hour, or until it has doubled in size.
While the dough is rising, preheat your oven to 375°F (190°C).
After the dough has risen, punch it down gently to remove excess air. Roll it out on a floured surface into a rectangle approximately 1/4 inch thick.
With a spatula or your fingers, spread a thin layer of softened butter evenly over the surface of the rolled-out dough. Then, sprinkle a mixture of cinnamon and sugar evenly over the buttered dough.
Starting from one long edge, roll the dough tightly toward the opposite edge to form a log. Pinch the edges to seal it, then cut the log into 12 equal pieces with a sharp knife or dental floss. Arrange the pieces in a greased baking dish.
Cover the rolls with a towel and allow them to rise for an additional 30 minutes until they puff up.
Bake the rolls in the preheated oven for 20-25 minutes, or until they turn a lovely golden brown color.
While the cinnamon rolls are baking, prepare the cream cheese glaze. In a medium bowl, combine the softened cream cheese, powdered sugar, vanilla extract, and 2 tablespoons of milk. Beat with a handheld mixer or whisk until the mixture turns smooth and creamy.
Once the cinnamon rolls are finished baking, remove them from the oven and let them cool slightly in the pan. Drizzle the cream cheese glaze generously over the warm rolls.