Preheat oven to 400°F. Lightly grease a 9x13-inch casserole dish with nonstick spray.
Place diced zucchini and bell pepper on a baking sheet. Toss with olive oil, salt, and pepper. Roast for 15–20 minutes until tender and slightly charred. Reduce oven temperature to 350°F.
In a small saucepan over low heat, combine sour cream, broth, chipotle peppers, and smoked paprika. Stir until smooth and warmed through. Season with salt and pepper. Set aside.
In a large skillet over medium heat, brown the ground beef. When halfway cooked, add chopped onion. Continue cooking until beef is fully browned and onion is soft. Stir in garlic and cook for 1 minute. Drain excess grease.
Reduce heat to low. Stir in black beans and green chiles. Add 1¼ cups of the chipotle cream sauce and mix to combine. Cook for 2 more minutes.
Spread 2 tablespoons of chipotle sauce on the bottom of the casserole dish.
Layer ¼ of the tortillas, ⅓ of the beef mixture, ⅓ of the roasted vegetables, and ¼ of the cheddar and Monterey Jack cheeses. Repeat layers two more times.
Finish with the remaining tortillas, remaining sauce, remaining cheeses, and Parmesan cheese on top.
Cover with foil and bake at 350°F for 25 minutes.
Remove foil and bake uncovered for another 10–12 minutes or until the cheese is golden and bubbling.
Let rest for 5–10 minutes before slicing and serving.