Preheat your oven to 375°F (190°C). Grease a 9x13 inch baking dish with olive oil and set aside.
Using a vegetable peeler or mandoline slicer, slice the zucchinis lengthwise into thin strips, resembling lasagna noodles.
Lay the zucchini slices on paper towels and sprinkle them with salt. Allow them to sit for 10 minutes to remove excess moisture, then pat dry.
In a mixing bowl, combine the shredded chicken, half of the cheddar cheese, half of the Monterey Jack cheese, cumin, chili powder, salt, and black pepper. Mix well.
Pour half of the enchilada sauce into the prepared baking dish, spreading it evenly.
Place a spoonful of the chicken mixture on a zucchini slice, roll it up, and place it seam side down in the baking dish. Repeat with the remaining zucchini slices and chicken mixture.
Drizzle the remaining enchilada sauce over the zucchini rolls.
Sprinkle the remaining cheddar and Monterey Jack cheeses over the top.
Bake in the preheated oven for 20 minutes, until the cheese is melted and bubbly.
While the enchiladas are baking, mix the sour cream with a small amount of water to thin it out for drizzling.
Remove the enchiladas from the oven, drizzle with sour cream, and garnish with fresh cilantro if desired.
Serve hot and enjoy your low-carb feast!