For the sauce: Combine all of the sauce ingredients in a saucepan. Bring to a simmer and cook until all of the vegetables are tender, about 15 minutes. If desired, you can puree with an immersion blender or an immersion blender for a smooth consistency. Season to taste with salt and pepper. Thin with water, if necessary. While the sauce is simmering, make the filling.
For the filling: Heat a 12-inch nonstick saute pan over medium heat. Add the onions and garlic and cook until the onions are translucent, about 4 minutes. Add the mushrooms and cook until they have released most of their liquid, about 6 minutes. Add a few tablespoons of water if the mushrooms get too dry. Add the spinach and cook until it is heated through. Combine the milk and the cornstarch to make a slurry. Add the milk mixture and bring to a simmer. Once the mixture comes to a simmer, the cornstarch will thicken the liquid. Cook for 1 minute. Add the cumin, chipotle, and lime juice and mix well. Remove from the heat and season, to taste, with salt and pepper. Cool slightly.
Preheat the oven to 375 degrees F.
Wrap the tortillas in a wet paper towel and microwave for 15 seconds to heat. Ladle 1/2 of the sauce into the bottom of a baking dish. Place a few tablespoons of the filling on each tortilla and roll into a cylinder. Place, seam side down in the dish. Repeat with the remaining tortillas and filling. Top with the remaining sauce and the cheese. Bake, uncovered, until heated through and bubbly, about 25 to 30 minutes.