Heat the milk until it reaches 100°F to 110°F. Transfer to a bowl, sprinkle the yeast and 1/2 teaspoon granulated sugar over the top, then gently swirl the bowl so some yeast settles into the liquid. Set aside for 10 minutes until the mixture becomes foamy and active.

In the bowl of a stand mixer, whisk together the flour, 1/4 cup cane sugar, salt, 1/2 teaspoon pumpkin pie spice, and 1/4 teaspoon cinnamon to distribute the dry ingredients. Add the foamy yeast mixture along with the whole egg, egg yolk, 4 tablespoons softened butter, and 1/3 cup pumpkin puree. Beat on medium-low speed for about 5 minutes until a smooth, elastic dough forms. Shape into a ball, lightly grease the mixing bowl, return the dough, then cover and let rise in a warm spot for 1 hour or until doubled in size.

Once risen, transfer the dough to a floured work surface and roll it into a rectangle measuring roughly 12 by 18 inches. Combine 1 cup packed brown sugar, 1/2 cup cane sugar, 1 tablespoon cinnamon, and 1/2 teaspoon pumpkin pie spice in a small bowl. Brush the rolled dough evenly with 4 tablespoons melted butter, then sprinkle the cinnamon-sugar mixture over the entire surface. Roll tightly from the long side to form a log, then cut into 12 equal pieces using thread or a serrated knife.

Place the rolls in a greased 9x13-inch baking dish, cover, and let rise for another 30 minutes. While they rise, preheat your oven to 350°F. Once the second rise is complete, uncover and bake for 25 to 30 minutes until the tops are golden brown and the rolls are cooked through. Remove from the oven and let cool for a few minutes.

While the rolls cool, beat together the cream cheese, 2 tablespoons softened butter, 2 tablespoons pumpkin puree, vanilla extract, 1/8 teaspoon cinnamon, 1/8 teaspoon pumpkin pie spice, and powdered sugar until smooth and creamy.

Spread the pumpkin cream cheese icing generously over the warm cinnamon rolls. Serve immediately while soft and gooey. If desired, sprinkle a light dusting of cinnamon on top before serving.