In a mixing bowl, stir together the warm milk, 1 tablespoon of the sugar, and the quick-rise yeast. Let the mixture sit for 5 minutes until it becomes foamy and bubbly on top.

Add the blotted pumpkin puree, melted butter, egg yolk, remaining 2 tablespoons sugar, salt, pumpkin pie spice, and cinnamon to the yeast mixture. Stir until thoroughly combined, then gradually add the flour, mixing with a wooden spoon until a shaggy dough comes together.

Turn the dough out onto a lightly floured surface and knead for 6 to 8 minutes, adding a little flour as needed, until the dough is smooth, elastic, and slightly tacky. It should spring back slowly when pressed with a finger.

Place the dough in a lightly greased bowl, cover with plastic wrap or a damp kitchen towel, and let it rise in a warm place for 30 to 40 minutes, or until doubled in size.

While the dough is rising, mix the brown sugar, cinnamon, and nutmeg in a small bowl. Line an 8-inch round cake pan with parchment paper and lightly grease the paper.

Punch down the risen dough and roll it into an 8 by 12-inch rectangle on a lightly floured surface. Spread the very soft butter evenly over the dough, leaving a 1/2-inch border along one long edge. Sprinkle the brown sugar mixture over the butter and press it in gently.

Starting from the long edge without the border, roll the dough tightly into a log and pinch the seam to seal. Cut the log into 6 even pieces, about 1 1/2 inches each, and place them cut-side up in the prepared pan.

Cover the pan loosely with plastic wrap and let the rolls rise for 25 to 30 minutes, until they look puffed and are just touching each other.

Preheat the oven to 350°F. Bake the rolls for 20 to 25 minutes, until golden brown and a toothpick inserted into the center comes out clean. Let them cool in the pan for 5 minutes.

In a small bowl, whisk the powdered sugar, maple syrup, heavy cream or milk, vanilla, and pinch of salt until smooth and pourable. Drizzle the glaze over the warm rolls.