Coat the pepper with 1/2 teaspoon of the oil. Roast directly on the grate of a gas burner over high heat or under a broiler, turning the pepper occasionally until charred all over. Put the pepper in a bowl while still hot and cover the bowl with plastic wrap. Let rest until cool enough to handle. Stem, seed, and peel the pepper, using a table knife to scrape away the charred skin. Coarsely chop the pepper and set aside.

In a nonreactive 5- to 6-quart Dutch oven, heat the remaining 3 tablespoons oil over medium-low heat. Add the onion and cook, stirring occasionally, until just soft, 8 to 10 minutes. Stir the chili powder, cumin, and coriander into the onions. Add the roasted pepper and cook for another minute. Add the broth and tomatoes and bring to a simmer over mediumhigh heat. Reduce the heat to low, cover, and simmer for 40 minutes.

Let cool briefly and then puree the soup in two or three batches in a blender or food processor. Rinse the pot and return the soup to the pot. If it is too thick, add some of the reserved tomato juice. Add the zucchini and cook for another 10 minutes over low heat.

Meanwhile, combine the sour cream, lime juice, and lime zest in a small bowl.

Season the soup to taste with salt and pepper. Serve garnished with the lime sour cream and the cilantro leaves.

Make Ahead: This soup stores beautifully and tastes better the second day. You can keep it in the refrigerator as long as you bring it to a boil every two days. Or you can stash it in the freezer for up to three months.

Be sure to puree in small batches and crack the blender lid slightly (or remove the center cap from the lid). Steam can build up once you start blending, and if the lid is on tight or the blender is overfilled, it will spray hot soup all over you and your kitchen. For protection, cover the top with a dishtowel while pureeing.