Proof the yeast (if using active dry). Warm the milk until it feels like a hot bath, not scalding. In a small bowl, stir together warm milk, a pinch of sugar, and the yeast. Let it sit for 5 to 10 minutes until foamy. If using instant yeast, you can skip this step and add it directly to the flour.
Make the dough. In a large mixing bowl, whisk 3 cups of flour with salt, cinnamon, and pumpkin pie spice. In a separate bowl, combine pumpkin puree, granulated sugar, egg, melted butter, and vanilla. Add the yeast mixture (or instant yeast) to the wet ingredients and stir. Pour the wet into the dry. Mix with a wooden spoon or dough hook until a shaggy dough forms. If it’s very sticky, add more flour 1 tablespoon at a time. The dough should be soft and slightly tacky, not gluey.
Knead. Knead by hand on a lightly floured counter for 6 to 8 minutes, or use a stand mixer with a dough hook for 5 to 6 minutes on medium-low. You’re looking for a smooth, elastic dough that bounces back when pressed with a finger.
First rise. Shape the dough into a ball and place in a lightly greased bowl. Cover with a clean towel or plastic wrap. Let it rise in a warm, draft-free spot until doubled, about 60 to 75 minutes. If your kitchen is cool, it might need 90 minutes. No rush.
Make the filling. Stir the soft butter, brown sugar, cinnamon, pumpkin pie spice, and salt until it looks like a thick paste. Set aside. Grease a 9-by-13-inch baking pan.
Roll it out. Turn the risen dough onto a lightly floured surface. Roll into a rectangle, roughly 12-by-16 inches. Spread the filling evenly over the dough, all the way to the edges on the long sides, leaving a small 1/2-inch border on one short side to help seal. Sprinkle nuts, if using.
Roll and slice. Starting from the short edge opposite the border, roll up the dough into a snug log. Pinch the seam. Use a sharp knife or unflavored dental floss to cut 12 even rolls. Tip: cut the log in half, then each half into 6 pieces to keep sizes close.
Second rise. Arrange the rolls in the greased pan with a little space between them. Cover and let rise until puffy and touching, 30 to 45 minutes. While they rise, heat the oven to 350°F (175°C).
Bake. Bake on the middle rack for 22 to 28 minutes. They’re done when the centers look set, the tops are lightly golden, and an instant-read thermometer in a center roll reads about 190°F/88°C. If the tops brown fast, tent with foil for the last 5 minutes.
Make the icing. Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, salt, and 1 tablespoon milk. Beat until creamy. Add more milk to thin or more powdered sugar to thicken. You want a spreadable glaze that gently melts over warm rolls.
Finish and serve. Spread icing over warm rolls (not scorching hot, give them 5 minutes to settle). Serve warm. Breathe in. It’s a good moment.