Heat a large cast-iron skillet over high heat until hot. Arrange the onion and garlic in the skillet in a single layer and cook, turning once, until charred, about 7 minutes.

Working in batches, if necessary, combine the chipotle, tomatoes, charred onion, and garlic in a blender and puree until smooth.

Transfer the tomato mixture to a large pot. Bring to a boil and cook, stirring, until the mixture has thickened, about 4 minutes. Pour in the broth, return to a boil, lower the heat, and simmer, covered, stirring occasionally, for 20 minutes.

Meanwhile, pour the oil for frying into a large heavy-bottomed pot to a depth of 2 inches. Place over medium heat and heat to 365 degrees F. Add the tortilla strips and fry until golden brown, about 1 minute. Using a slotted spoon, transfer the strips to a paper towel-lined plate and sprinkle with salt. Repeat with the pasilla strips, frying them for 10 seconds, and transfer to the plate.

When ready to serve the soup, stir in the 2 teaspoons salt and the lime juice. Divide the tortilla strips and cheese among soup bowls and ladle the tomato broth over them. Garnish with the pasilla strips, scallion, and cilantro. Serve immediately.