Steam the potatoes and carrots separately until they are just tender to the bite, but not too soft, about 10 minutes.
Heat the oil in a large skillet. Cook and stir the onions until they are translucent, about 10 minutes. Add the garlic and cook and stir another minute or so. Stir in the potatoes and carrots and the spinach. Cover the pan and let the arugula wilt a few minutes. Season to taste with salt and pepper.
Preheat the oven to 350 degrees. Brush some oil in a deep casserole dish. Ladle about 1/2 cup of sauce in the bottom.
Lay a tortilla down, sprinkle a little about 1/3 cup of the vegetable mixture on top and then about a tablespoon of the cotija cheese. Spread with a few tablespoons of sauce. Lay down another tortilla, follow with vegetables and cheese and sauce, continuing this stacking and layering until you are out of filling. End with a tortilla dipped in the sauce. Sprinkle with more cheese.
If there are leftover vegetables, toss them with some of the mole, and spoon them around the sides of the stack.
Bake until the sauce begins to bubble around the edges, about 30 minutes.