In a large skillet, cook the garlic in the oil over moderate heat, stirring, until it is fragrant, stir in the Swiss chard stems and 1/4 cup water, and cook the mixture, covered, for 5 minutes. Add the leaves and cook the mixture, covered, stirring occasionally, for 3 to 5 minutes, or until the leaves are tender. Drain the Swiss chard mixture in a bowl toss it with the shredded chicken and salt and pepper, to taste.
Preheat oven to 350 degrees F.
In a skillet, heat 1/4 inch of the oil over moderately high heat until it is hot but not smoking. In it, fry the tortillas, 1 at a time, turning them, 3 to 4 seconds, or until they are softened, and transfer them with tongs as they are fried to paper towels to drain.
In a bowl, thin the tomato sauce with the broth, spoon about 1/3 cup of it into the bottom of a greased 13 by 9-inch baking dish, and arrange 4 of the tortillas in one layer over it. Spread the tortillas with half the chicken mixture and half the Monterey Jack, spoon about 1/2 cup of the remaining sauce over the mixture, and cover it with 4 of the remaining tortillas in one layer. Spread the tortillas with the remaining chicken mixture and the remaining Monterey Jack, top the mixture with 1/2 cup of the remaining sauce, and cover it with the remaining 4 tortillas. Pour the remaining sauce evenly over the tortillas and sprinkle it with the Parmesan.
Bake the enchiladas, covered with foil, in the middle the oven for 15 minutes, remove the foil, bake the enchiladas, uncovered, for 5 to 10 minutes more, or until the cheese is bubbling.
In a blender, puree the tomatoes with the onion, the garlic, and the chiles.
In a large skillet, heat the oil over moderately high heat until it is hot but not smoking, add the tomato puree, and cook the mixture, stirring occasionally, for 5 minutes.
Season the sauce with salt and black pepper.
Yield: 2 1/2 cups