Position an oven rack in the center and preheat the oven to 400°F (204°C).
Heat the olive oil in a large skillet over medium heat. Add the minced garlic and sauté for about 30 seconds, just until fragrant.
Add the corn and cook until heated through and lightly tender. Stir in the diced green chiles.
Add the shredded chicken and 3 tablespoons of sliced green onions. Stir until everything is evenly combined and heated through. Remove from the heat and set aside.
To prepare the avocado cream, place the avocado, salsa verde, and sour cream in a blender. Blend until completely smooth and creamy. Refrigerate until serving.
Rinse the blender if necessary. Add the pumpkin puree, garlic cloves, jalapeño, cumin, black pepper, kosher salt, chicken broth, and water.
Blend until you have a completely smooth pumpkin enchilada sauce.
Spread approximately 1 cup of pumpkin sauce across the bottom of a 9 x 13-inch baking dish.
Warm the tortillas briefly in a dry skillet over medium heat until soft and flexible. This helps prevent cracking during rolling.
Place a tortilla on a clean work surface. Spoon approximately 1/3 cup of chicken filling across the tortilla and roll it tightly.
Place the rolled tortilla seam-side down in the prepared baking dish. Repeat with the remaining tortillas and filling.
Pour the remaining pumpkin sauce evenly over the Pumpkin Chicken Enchiladas.
Sprinkle the grated Monterey Jack evenly over the top.
Cover the baking dish with aluminum foil and bake for 20–25 minutes, until the enchiladas are thoroughly heated and the cheese is melted and bubbling.
Remove from the oven and garnish with Cotija-style cheese, fresh cilantro, and sliced green onions.
Serve warm with the chilled avocado cream spooned or drizzled over each portion.