• In a large mixing bowl, combine 2 cups of flour, sugar, dry yeast, and salt. Give it a good stir to blend everything together. Warm the water and butter in a microwave-safe bowl for about 15 seconds at a time, stirring between intervals, until the mixture is very warm but still comfortable to touch (around 120°F to 130°F). Don’t worry if the butter isn’t fully melted. Add this to the flour mixture along with the egg.
• Using a mixer, beat the mixture on medium speed for about 2 minutes, scraping down the sides occasionally. Add another cup of flour and beat on high speed for 2 more minutes, scraping the bowl as needed. Gradually stir in just enough of the remaining flour until a soft dough forms that pulls away from the sides of the bowl.
• Transfer the dough to a lightly floured surface and knead it until it’s smooth, elastic, and bounces back when gently pressed with two fingers. This should take about 6–8 minutes. Cover the dough with a clean kitchen towel and let it rest for 10 minutes.

Prepare the Filling

• While the dough rests, mix sugar, pumpkin pie spice, and pumpkin puree in a small bowl. Set the filling aside.

Assemble the Rolls

• Roll out the dough into a 15 x 10-inch rectangle. Spread the pumpkin filling evenly over the surface, leaving about a ½-inch border along the long edges. Starting from one long side, roll the dough tightly into a log and pinch the seam to seal it. Cut the log into 12 even slices.
• Arrange the slices, cut side down, in a greased 13 x 9-inch baking pan.

Baking Options

To bake right away:

• Cover the pan with a kitchen towel and let the rolls rise in a warm spot until doubled in size, about 1 hour. Bake in a preheated 350°F oven for 25–30 minutes, or until the rolls are beautifully golden. Let them cool on a wire rack for at least 20 minutes before frosting.

To bake the next day:

• Cover the pan with plastic wrap and refrigerate overnight. In the morning, take the pan out of the fridge and let it sit at room temperature for 30–45 minutes. Bake in a preheated 350°F oven for 25–30 minutes, or until golden brown. Allow the rolls to cool for 10–15 minutes before frosting.

Frosting the Rolls

• In a large bowl, beat the cream cheese, butter, and vanilla together until smooth. Gradually add 1 cup of sifted powdered sugar at a time, beating well after each addition. If needed, add milk ½ tablespoon at a time until the frosting reaches your desired consistency. Spread the frosting over the rolls while they’re still slightly warm.
• Store any leftover rolls in the refrigerator.