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1
Peel the garlic cloves and reserve 2 for the chile sauce.
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2
Slice the remaining garlic.
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3
In a 7 to 8 quart heavy kettle bring water and broth just to a boil with sliced garlic and pork.
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4
Skim the surface and add oregano.
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5
Gently simmer pork, uncovered, until tender, about 1 1/2 hours.
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6
While pork is simmering, wearing protective gloves, discard stems from chiles, and in a bowl, combine chiles with boiling-hot water.
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7
Soak chiles, turning them occasionally, for 30 minutes.
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8
Cut onion into large pieces and in a blender puree with chiles and soaking liquid, reserved 2 cloves of garlic, and 2 teaspoons salt until smooth.
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9
Transfer pork with tongs to a cutting board and reserve broth mixture.
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10
Using 2 forks, shred the pork.
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11
Discard the pork bones.
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12
Rinse and drain hominy.
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13
Return pork to broth mixture and add chile sauce, hominy, and remaining teaspoon salt.
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14
Simmer posole 30 minutes and, if necessary, season with salt.
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15
Posole may be made 2 days ahead and chilled, covered.
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16
While posole is simmering, stack tortillas and halve.
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17
Cut halves crosswise into thin strips.
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18
In a 9 to 10-inch skillet heat 1/2 inch oil until hot but not smoking and fry tortilla strips in 3 or 4 batches, stirring occasionally, until golden, 1 to 2 minutes.
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19
Transfer tortilla strips with a slotted spoon as fried to brown paper or paper towels to drain.
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20
Transfer tortilla strips to a bowl.
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21
Tortilla strips may be made 1 day ahead and kept, covered, at room temperature.
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22
Serve posole with tortilla strips and bowls of accompaniments.
