Put the chicken in a saucepan with the half onion, 2 whole garlic cloves and 2 teaspoons salt. Cover with 6 cups cold water, bring to a bare simmer and cook uncovered 25 to 30 minutes, until the meat pulls easily from the bone. Skim any foam as it rises.

Lift the chicken out and let it cool enough to handle. Strain the broth and reserve 1.5 cups for the sauce. Pull the meat off the bones and shred it by hand into thick strands, not fine threads. Season with a pinch of salt and keep warm.

Heat a dry comal or cast iron skillet over medium. Press the opened guajillo and ancho chiles flat against the hot surface for 5 to 10 seconds per side, just until they smell toasty and turn fragrant. Do not let them smoke or darken, or the sauce will be bitter.

Transfer the toasted chiles to a bowl, cover with hot water and soak 15 minutes until fully pliable. Meanwhile, roast the tomatoes on the same comal, turning, until blistered and blackened in spots, about 8 minutes.

Drain the chiles and put them in the blender with the roasted tomatoes, remaining 2 garlic cloves, cumin, oregano, 1 teaspoon salt and 1 cup of the reserved broth. Blend 2 full minutes until completely smooth, then pass through a fine mesh strainer, pushing with a spoon and discarding the skins left behind.

Heat 2 tablespoons of the lard in a skillet over medium-high until it shimmers. Pour in the strained sauce all at once, standing back as it spatters. Fry 8 to 10 minutes, stirring often, until it darkens, thickens and the raw chile smell is gone. Loosen with the remaining broth to the consistency of heavy cream and taste for salt. Pour into a wide shallow bowl and keep warm.

Wipe the skillet and heat the remaining lard over medium-high. Slide in one tortilla at a time and fry 5 to 8 seconds per side, just until soft and flexible but not crisp. Drain on paper towels and stack them. This fat barrier is what keeps the tortillas from falling apart.

Working one at a time, dip a tortilla fully through the warm sauce, lay it on a plate, put a generous line of shredded chicken down the center and roll it up. Place seam side down on the serving platter. Repeat with all 12 tortillas, snugging them against each other.

Ladle the remaining warm sauce over the rolled enchiladas and scatter the queso fresco on top. If you want the cheese melted, slide the dish into a 350 F oven for 15 minutes, no longer.

Finish with drizzled crema, rings of raw white onion and chopped cilantro. Bring to the table at once and eat while the tortillas still have structure.