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1
Roast the green chiles directly over a gas flame or under a broiler, turning, until the skin is fully blackened on all sides. Transfer to a bowl, cover tightly, and leave for 15 minutes. Peel away the charred skin, slit each chile, and remove seeds and veins. Roughly chop. The flesh should be soft, smoky, and distinctly green — not pale or raw-smelling.
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2
Place the tomatoes on a dry comal or heavy skillet over high heat and char them on all sides until the skin is blistered and darkened and the flesh has softened. Remove and chop roughly. In a blender, combine the charred tomatoes, roasted chiles, and garlic. Blend to a coarse purée. The colour should be a deep, mottled green-red and the aroma should be smoky and sharp.
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3
Heat the oil in a large, heavy pot over high heat until it shimmers. Season the beef chunks with salt and add them in a single layer — work in batches to avoid crowding. Sear without moving until a deep mahogany crust forms on each side. This is where the dish lives or dies: without a proper Maillard crust on every surface, the broth will be pale and the flavour thin. The beef should release from the pan cleanly and the fond on the pot base should be dark and fragrant.
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4
Reduce the heat to medium. Add the cumin to the pot and stir for 30 seconds until it blooms and the spice is clearly perceptible as a warm, toasty note in the steam. Pour in the chile-tomato purée and stir to lift the fond from the base of the pot.
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5
Return all the beef to the pot. Add enough water or broth to submerge the meat by at least 2 cm. Bring to a gentle simmer, then reduce the heat to low. Cover and braise for a minimum of 90 minutes, checking periodically that the liquid remains at a quiet simmer and never a rolling boil. The beef is done when a chunk yields without resistance to gentle pressure and the broth has taken on colour and body from the chile and tomato. Total braising time is typically 90 minutes to 2 hours.
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6
Taste the broth and adjust salt. The caldillo should be clean, green-chile forward, and savoury — lighter and fresher than a dried-chile stew. Serve in deep bowls with generous broth, accompanied by warm flour tortillas and frijoles.