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1
Heat the oil in a large saucepan or Dutch oven over medium heat until shimmering.
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2
Add the onion, carrot, celery, and bell pepper and season with salt and pepper.
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3
Cook, stirring occasionally, until the vegetables have softened, about 6 minutes.
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4
Add the garlic, chili powder, coriander, cumin, oregano, paprika, and cayenne and cook, stirring occasionally, until fragrant, about 2 minutes.
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5
Add the broth, water, tomatoes, and measured salt and pepper, stir to combine, and bring to a boil.
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6
Reduce the heat to low, add the tortillas, and stir to combine.
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7
Simmer, stirring occasionally, until the tortillas have disintegrated and the soup has thickened, about 1 hour.
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8
Meanwhile, make the tortilla strips.
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9
Heat the oil in a large frying pan over medium-high heat until shimmering but not smoking (about 350 degrees F on a deep-frying/candy thermometer), about 6 minutes.
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10
Meanwhile, stack the tortillas on a cutting board.
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11
Cut the stack in half, then cut crosswise into 1/4-inch strips; set aside.
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12
Line a baking sheet with paper towels; set aside.
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13
When the oil is ready, add half of the tortilla strips and fry, stirring occasionally, until golden brown and crisp, about 2 to 2 1/2 minutes.
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14
Remove with a slotted spoon to the prepared baking sheet and season with salt and pepper.
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15
Repeat with the remaining tortilla strips; set aside.
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16
When the soup is ready, add the chicken and cream and stir to combine.
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17
Simmer until the flavors meld, about 15 minutes.
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18
Taste and season with salt and pepper as needed.
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19
Serve the soup topped with the tortilla strips, passing any desired garnishes on the side.
