In the bowl of a stand mixer, whisk warm milk, yeast, and 1 tablespoon of the sugar. Let sit for 5 to 7 minutes until foamy. Add the remaining sugar, blotted pumpkin puree, melted butter, egg, salt, and 2 cups of flour. Beat on low with the dough hook, then gradually add the remaining flour until a soft, slightly tacky dough forms.

Knead on medium-low speed for 6 to 8 minutes until smooth and elastic. Transfer dough into an oiled bowl, cover with plastic wrap, and let rise in a warm spot for 60 to 75 minutes, or until doubled in volume.

Punch down dough and roll out on a lightly floured surface into a 14x18-inch rectangle. Spread softened butter evenly over the dough. In a small bowl, mix brown sugar, cinnamon, and pumpkin pie spice; sprinkle generously over the butter. Roll up tightly into a log starting from the long edge, then slice into 12 equal rolls using unflavored dental floss or a sharp serrated knife.

Place rolls cut-side up in a greased 9x13-inch baking dish. Cover and let rise for 30 minutes until puffy. Just before baking, gently warm 1/3 cup of heavy cream and pour it between and over the rolls (this bakery trick guarantees gooey, melt-in-your-mouth centers!).

Bake in a preheated oven at 350°F (175°C) for 22 to 26 minutes until golden brown on top and the internal temperature reaches 190°F. If tops brown too quickly, tent loosely with foil.

While rolls bake, beat cream cheese, butter, powdered sugar, maple syrup, and vanilla until fluffy and smooth. Spread generously over warm rolls so the icing melts into the cracks. Serve warm!