For the Salsa: Adjust oven rack to upper-middle position and preheat oven broiler to high setting. Line a rimmed baking sheet with aluminum foil, then add tomato and onion layers spread in an even layer. Broil until well charred, 3 to 5 minutes. Flip and broil until second side is charred, about 3 more minutes. Set baking sheet aside to cool.

In a blender jar, add charred ingredients, black garlic, chiles, and chicken stock. Blend on high until smooth, about 1 minute. Season with salt to taste.

In a medium saucepan, add sauce and set it over low heat until warmed through, about 5 minutes. Hold sauce warm over low heat while preparing tortillas. Remove foil from cooled baking sheet and line now-empty sheet with a layer of paper towels.

In an 8- or 10-inch skillet, melt 1 teaspoon lard over medium heat. Add 1 tortilla and cook until softened, about 10 seconds. Flip and cook for 10 seconds longer. Transfer to paper towel–lined sheet. Repeat with remaining tortillas, adding a lard, a teaspoon at a time,as the skillet dries out.

Add shredded chicken to now-empty skillet and toss occasionally until warmed through.

One at a time, using tongs, dip tortillas into the sauce, then transfer to a plate. Fill tortillas with shredded chicken, then roll tortilla around chicken. Transfer to a serving platter or individual plates. Spoon remaining salsa over the enchiladas. Serve with onion, cabbage, crema, queso, and cilantro.