Start by preheating your oven to 425°F so it's fully hot by the time you're ready to bake. In a large bowl, mix the shredded rotisserie chicken with the sour cream and sliced green onions. Season it generously with salt and pepper, then set the bowl aside while you make the sauce.
Add the pumpkin puree, garlic, jalapeño, chili powder, chicken broth, cinnamon, and a good pinch of salt and pepper to your blender. Blend everything until it's completely smooth, with no visible garlic or jalapeño chunks left. Taste it carefully, since this sauce coats every part of the dish.
Pour about a cup of the pumpkin sauce into the bottom of your baking dish, then pour another cup onto a shallow plate for dipping. Working one at a time, dip each tortilla in the sauce on both sides. This step keeps the tortillas soft and flavorful instead of dry once baked.
Lay a sauce-dipped tortilla flat and spoon about a third of a cup of the chicken filling down the center. Roll it up snugly and place it seam-side down in the baking dish. Repeat with the remaining tortillas until your dish is packed with neat little rolls.
Pour the rest of the pumpkin sauce evenly over the rolled enchiladas, making sure every tortilla is covered. Sprinkle the shredded Monterey Jack cheese generously across the top. This layer is what turns golden and bubbly in the oven.
Slide the dish into your preheated oven and bake for 25 to 30 minutes, until the cheese is melted and starting to turn golden and the sauce is visibly bubbling at the edges. Let the dish rest for 5 minutes before serving so it sets slightly.