Preheat oven to 350 degrees. Spread 1/3 c. enchilada sauce in the bottom of a 9 x 13-inch baking dish.
In a large skillet, heat olive oil over medium heat. Add onion and season with salt. Cook until soft, about 5 minutes. Add garlic, cumin and chili powder, stir until combined.
Add shredded chicken and 1 cup enchilada sauce and stir until heated through. Remove from heat.
On a cutting board, use a vegetable peeler to make thin slices of zucchini.
Lay out three slices of zucchini, slightly overlapping, and place a spoonful of chicken mixture on top. Roll up and transfer to prepared baking dish seam side down. Repeat with remaining zucchini and chicken mixture.
Spoon remaining 1/3 cup enchilada sauce over zucchini enchiladas and sprinkle with both cheeses.
Bake for 20-25 minutes, until cheese is melted and sauce is bubbly.