Proof the yeast: In a small bowl, combine warm milk and 1 tsp sugar. Sprinkle yeast on top and let sit for 5–10 minutes until foamy.

In a large bowl, whisk 3 1/4 cups flour, salt, cinnamon, and nutmeg. In another bowl, mix pumpkin puree, sugar, melted butter, egg, vanilla, and the milk/yeast mixture. Combine wet into dry and stir until a shaggy dough forms.

Knead the dough on a lightly floured surface for 6–8 minutes until smooth and slightly tacky.

Place dough in a lightly oiled bowl, cover, and let rise in a warm spot for 60–90 minutes, or until doubled.

Prepare the filling by mixing softened butter, brown sugar, cinnamon, pumpkin pie spice, and salt until spreadable.

Punch down dough and roll it into a 12x16-inch rectangle.

Spread the filling evenly over the dough, leaving a 1/2-inch border on one long edge. Roll tightly from the opposite long side, pinching the seam to seal.

Trim the ends and cut into 12 even pieces using dental floss or a sharp knife.

Place in a buttered 9x13-inch pan, leaving slight space between rolls.

Cover and let rise for 30–45 minutes until puffy.

Preheat the oven to 350°F (175°C) and bake rolls for 22–26 minutes until lightly golden and centers are set.

Brown the butter: Melt 1/2 cup butter in a light-colored saucepan over medium heat. Cook, stirring until milk solids turn amber and smell nutty (4–6 minutes). Transfer to a bowl to stop cooking and cool for 10 minutes.

For the frosting, beat cream cheese until smooth. Add cooled brown butter, powdered sugar, vanilla, and salt. Mix until fluffy, adding milk/cream 1 tsp at a time to reach a spreadable glaze.

Spread frosting over warm rolls so it melts into the swirls.