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1
Slice the tortillas in half and then into 1/8-inch-wide strips. Heat 1/3 cup of the vegetable oil in a medium-size (8-to-9 inch) skillet over medium-high. When hot, add about 1/3 of the tortilla strips and fry, turning frequently, until they are crisp on all sides. Remove with a slotted spoon and drain on paper towels. Fry the remaining strips in 2 batches.
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2
Cut chiles into rough 1-inch squares using kitchen shears. Reduce the heat under the oil to medium-low, let cool a minute, then fry the squares very briefly to toast them, 3 or 4 seconds; immediately remove and drain on paper towels. Place 1/3 of the chiles in a small bowl, cover with hot water and let rehydrate for 30 minutes, stirring regularly to ensure even soaking. Drain and discard the water. Set aside the remaining fried chiles.
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3
Roast the garlic and tomato on a baking sheet 4 inches below a very hot broiler until blackened and blistered on one side, about 6 minutes; flip and broil the other side. Cool, then peel both, collecting any juices. Note: Alternately, substitute a 14.5-ounce can of tomatoes (drained) and roast the garlic in a dry skillet on the stovetop.
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4
In a medium-size (4-quart) pot, heat the remaining 1 tablespoon of oil over medium-low. Add the onion and fry until brown, about 10 minutes. Place the rehydrated chiles in a food processor or blender along with the roasted garlic, tomato and 1 cup of the broth; puree until smooth. Raise the temperature under the pot to medium-high, and, when noticeably hotter, press the tomato-chile puree through a medium-mesh strainer into the fried onion. Stir for several minutes as the mixture thickens and darkens. Mix in the remaining 5 cups of broth, then simmer uncovered over medium-low, stirring occasionally, for 30 minutes. Season with salt.
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5
Set out the garnishes: Make mounds of the fried tortilla strips, fried chiles, cheese and lime on a large platter. Just before serving, reheat the soup, add the sliced chard and simmer until the chard is tender, 5 or 6 minutes. Ladle into warm soup bowls and pass the garnishes for each guest to use al gusto.
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6
Notes for advance preparation - The soup itself can be prepared several days ahead, but the chard will be freshest if you add it only as you're reheating the soup in the last few minutes. The fried tortillas will keep for a day wrapped in foil on the counter. Reheat the broth and set out the garnishes just before serving.
