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1
Rinse diced pork under cold water until water runs clear.
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2
Transfer pork a large stock pot over medium-high heat; add 8 cups cold water.
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3
Bring to a simmer; skim off and discard foam and solids that float to surface.
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4
Stir in garlic, bay leaves, onion, cumin, and 1 tablespoon salt.
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5
Turn heat to medium to keep soup at a light simmer.
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6
Cover and simmer 90 minutes (do not boil).
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7
Periodically skim foam from surface.
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8
Meanwhile, remove and discard stems, seeds, and large veins from dried chiles.
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9
Break into large pieces in a medium saucepan and add 3 cups water.
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10
Top with sweet onion, tomatoes, and garlic cloves, keeping chiles submerged.
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11
Cover and simmer 10 minutes, then remove from heat and set aside 15 to 20 minutes.
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12
Working in 2 batches, puree chile mixture with cooking liquid in a blender until smooth.
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13
Pour mixture through a fine-mesh sieve into soup pot, pressing solids with back of spoon to extract liquid.
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14
Simmer soup for 90 minutes, then stir in black pepper, oregano, and hominy.
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15
Taste and season with additional salt, if desired.
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16
Remove a piece of pork and taste for doneness.
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17
If meat is not tender, simmer 15 to 20 minutes more.
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18
Serve hot soup with garnishes for topping.