Preparation

• Roast the poblanos over a gas burner, a hot grill fire, or on a foil-lined baking sheet under the broiler, turning with tongs, until blackened or blistered all over, 6 to 10 minutes. Immediately put them in a bowl, cover, and let steam for 15 minutes. Once cooled, peel the skin, then split open, remove the stems, seeds, and ribs (reserve the ribs), and coarsely chop.
• Heat the olive oil in a 12-inch skillet over medium heat. Add the onions and garlic and cook, stirring, until softened, about 8 minutes. Add the poblanos and 2 tsp. salt and cook, stirring, for 2 minutes. Add 2 cups of the chicken broth, bring to a simmer, and cook for 3 minutes.
• In a blender, purée about one-third of the soup until very smooth, about 2 minutes.
• Set a medium-mesh strainer over a large bowl and force the purée through it with a silicone spatula. Repeat with the rest of the soup in 2 more batches. Taste, and if you would like more heat, reblend a cup of the purée with the reserved poblano ribs to taste, then stir it back into the purée. Stir in the cream and the remaining 1 cup chicken broth, thinning with additional chicken broth, if necessary. Cover and refrigerate until cold, at least 4 hours.
• Heat the vegetable oil in a 2-quart saucepan over medium heat until shimmering hot. Stack the tortillas on top of each other and cut in half. Stack the halves and cut crosswise into very thin strips. Working in 2 batches, fry the tortilla strips, turning them with a slotted spoon, until golden, about 1-1/2 minutes per batch. Transfer to paper towels to drain and sprinkle with salt.
• Just before serving, season the soup to taste with additional salt, if needed. Serve garnished with the tortilla strips.

Make Ahead Tips

The finished soup can be refrigerated, covered, for up to 2 days. Adjust the seasoning and garnish just before serving.

The tortilla strips can be made 1 day ahead, cooled, and stored in a zip-top bag.