Make the dough: Pour warm water into a large mixing bowl and sprinkle yeast over top. Allow to stand until yeast begins to form a creamy foam, 5 to 10 minutes.
Add pumpkin puree, sugar, evaporated milk, olive oil, and egg to the yeast mixture; mix until thoroughly combined. Stir in pumpkin pie spice, then mix in about 5 cups of flour, or as needed, until a stiff dough forms.
Turn dough out onto a floured work surface and knead until smooth and elastic, but still slightly sticky, about 8 minutes. Form dough into a ball, then place in an oiled bowl, cover with a cloth, and let rise in a warm place for about 45 minutes. (The dough will rise, but it won’t double.)
Preheat the oven to 350 degrees F (175 degrees C). Grease a 9×13-inch baking dish.
Punch down the dough, then roll it out on a floured work surface to an 18×26-inch rectangle. Brush the top with melted butter.
Make the filling: Mix together brown sugar and pumpkin pie spice in a small bowl; sprinkle evenly over the buttered dough. Start at the longer edge and roll dough over filling into a log. Pinch the seam closed, then use a serrated knife to cut the log into 12 equal rolls. Transfer rolls to the prepared baking dish with the cut-sides facing up.
Bake in the preheated oven until light golden brown on the edges, 30 to 40 minutes.
While the rolls are baking, make the glaze: Beat confectioners’ sugar, milk, butter, cream cheese, and vanilla in a bowl until well combined.
Remove pumpkin rolls from the oven and immediately spread glaze over top.
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