Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment and spray with cooking spray.

Add poblano chile, onion, and nopales in a skillet over medium-high heat. Cook until chile and onion are soft, 3 to 5 minutes.

Place 4 tortillas on a microwave-safe plate and cover with a damp paper towel. Heat until soft, about 30 seconds. Repeat with remaining tortillas.

Place 1 tortilla on a work surface. Spoon 2 tablespoons each of nopales mixture, Monterey Jack cheese, and black beans on top and fold in sides. Place chimichanga on the prepared baking sheet seam-side down. Repeat with remaining fillings and tortillas.

Bake in the preheated oven until golden brown, turning halfway through, 15 to 20 minutes.