Make the dough: In a stand mixer fitted with a dough hook combine bread flour, granulated sugar, salt, instant yeast, pumpkin pie spice, warmed milk, pumpkin puree, and eggs. Mix on low speed until everything comes together into a shaggy dough. Increase to medium speed and knead for a few minutes until the dough smooths out.
Add the butter: With the mixer running on medium speed slowly add the softened butter a few pieces at a time waiting for each addition to fully incorporate before adding the next. Continue kneading until the butter is fully incorporated and the dough is smooth, elastic, and passes the windowpane test.
First rise: Shape into a taut ball and place in a lightly oiled bowl. Cover and rise at room temperature until doubled in size, about 1 to 1.5 hours.
Make the filling: While the dough rises combine softened butter, dark brown sugar, cinnamon, pumpkin pie spice, and salt and mix into a smooth spreadable paste. Set aside.
Roll out: Turn the risen dough onto a lightly floured surface and roll into a 28x16 inch rectangle with even thickness throughout.
Fill: Spread the cinnamon sugar filling all the way to every edge. Don't leave any bare spots.
Roll and cut: Starting from the short edge roll tightly into a log with even tension throughout. Trim the ends. Cut into 10-12 rolls, 1 to 1.5 inches thick using a sharp knife or unflavored dental floss.
Arrange and proof: Place rolls cut side up in the baking pan — 8 fit in a 9x13 inch pan. Cover and proof until noticeably puffy and sides are just touching, about 1 hour.
Optional heavy cream: Pour ½ cup heavy cream evenly over the proofed rolls. The cream creates steam and keeps everything especially soft and pillowy. I particularly recommended if you use a convection oven but the rolls will still be soft without the cream!
Bake: Preheat oven to 350°F. Bake for 22-25 minutes until deep golden brown and internal temperature reaches 190°F.
Make the frosting: Dissolve instant espresso powder in 1 tsp hot water and let cool slightly. Beat softened cream cheese and softened butter until completely smooth. Add powdered sugar and espresso mixture and beat until creamy. Taste and add more espresso if you want a stronger flavor.
Frost: Spread generously over warm rolls and serve immediately.