Proof the yeast: In a large stand mixer bowl, whisk warm whole milk (110°F), 1 tablespoon of the sugar, and active dry yeast. Let sit for 5 to 7 minutes until frothy and bubbly.

Knead the pumpkin dough: Add the remaining sugar, blotted pumpkin puree, room-temperature egg, melted butter, pumpkin pie spice, salt, and 3 cups of flour. Fitted with the dough hook, knead on low speed, gradually adding the remaining flour until a soft, supple, slightly tacky dough forms (about 6 to 8 minutes).

First rise: Shape dough into a smooth ball and place in a greased bowl. Cover with a warm, damp towel and let rise in a warm spot for 60 to 75 minutes, or until doubled in size.

Roll and fill: Turn dough out onto a lightly floured surface. Roll into a 12x18-inch rectangle. Spread softened butter evenly over the dough, leaving a 1/2-inch border. Toss brown sugar with cinnamon and pumpkin pie spice, then sprinkle evenly over the butter, gently patting it in.

Slice and second rise: Starting from the long edge, roll the dough tightly into an 18-inch cylinder. Using unflavored dental floss or clean baker's twine, slice into 12 equal rounds. Place cut-sides up in a buttered 9x13-inch ceramic baking dish. Cover and let rise for 30 to 45 minutes until puffed and touching.

Warm cream soak & bake: Preheat oven to 350°F (175°C). Just before baking, pour 1/3 cup of warm heavy cream evenly over the tops and between the rolls (this is the bakery secret for ultra-gooey, soft centers). Bake for 23 to 27 minutes until golden brown on top.

Make maple icing and glaze: While rolls bake, beat softened cream cheese, butter, powdered sugar, maple syrup, vanilla, and a pinch of salt until silky and fluffy. Spread half of the icing over the rolls while warm so it melts into every crevice, then spread the remaining icing just before serving. Enjoy warm!