Preheat the oven to 350°F (175°C) and spray a 9x13-inch baking dish with cooking spray; set aside.
Heat 1 to 2 tablespoons olive oil in a large skillet over medium heat. Add the finely diced onion and sauté for 3–4 minutes until softened and translucent, stirring frequently.
While the onion cooks, use a Y-peeler to slice each zucchini lengthwise into very thin strips. Aim for about 36 strips total. Lay the slices on paper towels to absorb excess moisture and set aside.
Add the minced garlic to the skillet and cook for 1 minute until fragrant, stirring constantly.
Stir in the drained black beans and corn, then add the chili powder, ground cumin, salt, and black pepper. Cook for about 1 minute to warm and combine flavors.
Add the shredded chicken, 1/3 of the enchilada sauce (about 3.3 oz), and 1/2 cup of the cheese to the skillet. Stir to combine and heat for about 1 minute. Taste and adjust seasoning if desired.
Spread the remaining 1/3 of the enchilada sauce evenly over the bottom of the prepared baking dish.
Assemble the roll-ups: lay three zucchini strips parallel and slightly overlapping. Spoon about 3 tablespoons of the filling on one end of the strips and carefully roll them up. Repeat until all filling is used (you should have approximately 12 roll-ups).
Place each roll-up seam-side down in the prepared pan. Drizzle the remaining 1/3 cup enchilada sauce over the top and sprinkle with the remaining 1/2 cup cheese.
Bake in the preheated oven for about 25 minutes, beginning to check at 20 minutes. The dish is done when the cheese is lightly golden and the zucchini is tender.
Optionally garnish with finely minced cilantro, sliced avocado, and a drizzle of Mexican crema before serving.