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1
Wipe the dried chiles clean, remove stems and seeds. Place in a small saucepan with the 2 cups of water and bring to a simmer. Cook 5 minutes.
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2
Transfer chiles and all cooking water to a blender. Add the chopped garlic and salt. Blend until smooth, then strain through a medium-mesh sieve, pressing the solids. Discard the fibrous residue.
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3
Heat the lard or oil in a wide, heavy skillet over medium-high heat to approximately 175°C / 347°F. Fry the tortilla pieces in uncrowded batches until light golden, 2–3 minutes per batch. Lift out and drain briefly on absorbent paper.
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4
Pour off excess oil from the pan, leaving a thin slick. Return all the fried tortilla pieces to the pan. Pour the strained chile sauce over them and set the heat to high.
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5
Cook, stirring occasionally, for approximately 8 minutes, until the sauce has reduced and the pieces are well coated but not disintegrating.
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6
Transfer to a warm serving dish or individual plates. Scatter with the finely chopped raw onion and the crumbled cheese. Serve at once.