Preheat oven to 425°F. Line a large rimmed baking sheet with parchment paper.
Spread the zucchini, onion, and broccoli in a single layer on the prepared baking sheet. Drizzle with olive oil; add garlic, cumin, chili powder, salt, and pepper. Toss to coat.
Roast the vegetables for about 20-25 minutes, or until tender and slightly charred, stirring halfway through.
Transfer the veggies to a large bowl. Add the black beans, corn, ¾ cup of the enchilada sauce, and 1 cup of the cheese. Stir to combine. Taste and season with additional salt and pepper or other spices, if desired.
Reduce the oven temperature to 350°F. Grease a 9 x 13-inch baking dish. Spread about ½ cup of the enchilada sauce in a thin layer in the bottom of the pan.
Spread some of the veggie and bean mixture in the center of each tortilla. Roll up and place seam-side down in the prepared baking dish.
Pour the remaining enchilada sauce over top. Sprinkle with remaining cheese.
Bake, uncovered, for about 20 minutes (or until the enchiladas are heated through and the edges of the tortillas are a bit crispy). Garnish with desired toppings and serve warm.