Preheat your oven to 425°F and lightly coat a 7-by-11-inch baking dish with cooking spray.
In a large skillet, heat 2 tablespoons olive oil over medium heat. Add the diced butternut squash and cook, covered, for 8-10 minutes or until tender and lightly browned, stirring occasionally. Next, add the poblano peppers and onion, cooking uncovered until softened, about 5 minutes more.
Stir in the black beans, 2 tablespoons chopped cilantro, and ancho chile powder. Let the mixture cool slightly—this will make assembling the enchiladas easier.
Warm the tortillas to make them pliable, then spoon about ½ cup of the squash filling into each. Roll tightly and place seam-side down in the prepared baking dish.
Pour the enchilada sauce evenly over the rolled tortillas and sprinkle with shredded cheese. Cover with foil and bake for 15 minutes. Remove the foil and bake an additional 5 minutes to let the cheese melt completely.
While the enchiladas bake, prepare the slaw by tossing the shredded cabbage with lime juice, the remaining 1 tablespoon olive oil, and 2 tablespoons cilantro.
Serve the enchiladas hot, topped with the refreshing slaw and extra cilantro if desired.