Set a skillet over medium heat. When hot, toast the chile pieces a few at a time, pressing them to the hot surface with a spatula until aromatic and lightened in color underneath—about 10 seconds per side. (If you see more than a whiff of smoke, they’re burning.) Transfer toasted chiles to a blender jar. Add the garlic, tomatoes with their juice, cumin and black pepper. Blend to a as smooth a consistency as possible. (A food processor will work, though it won’t completely puree the chile.)
Heat the oil in a medium-large (5- to 6-quart) saucepan over medium-high heat. Set a medium-mesh strainer over the pot and pour in the sauce. Press through the strainer to remove bits of skin, remove the strainer, then stir the sauce until it’s reduced to the consistency of tomato paste, 5 to 7 minutes. Pour in the broth, reduce the heat to medium-low and simmer for 10 minutes while you prepare the tortillas, filling and toppings.
Lay out the tortillas on a baking sheet and spray or brush lightly on both sides with oil; stack them in twos. Slide the tortillas into the oven and bake just long enough to make them soft and pliable, about 3 minutes. Remove from the oven and stack them in a single pile; cover with a kitchen towel to keep warm.
Taste and season the sauce with salt, usually about 1 ½ teaspoons, and the sugar. Stir in additional broth if the sauce has thickened beyond the consistency of light cream soup. Spread about ½ cup sauce over the bottom of a 13x9-inch baking dish. Stir another ½ cup into the chicken. Lay out a warm tortilla, top with a portion of chicken and roll up. Lay in the baking dish, then continue filling and rolling tortillas until all are used. Ladle the remaining sauce over the enchiladas and sprinkle with cheese.
Bake 10 to 15 minutes, until the cheese is starting to brown (the chicken should be warm by then). Sprinkle with onion rings and cilantro sprigs, and you’re ready for dinner.