Whisk yogurt, 1 tablespoon cilantro, and lime juice together in bowl. Season with salt and pepper to taste. Cover and refrigerate until needed.

Adjust oven rack 3 inches from broiler element and heat broiler. Spread half of peppers skin side up on aluminum foil-lined baking sheet. Broil until skin is charred and puffed but flesh is still firm, 8 to 10 minutes, rotating sheet halfway through broiling. Transfer broiled peppers to bowl, cover with plastic wrap or foil, and let steam until skins peel off easily, 10 to 15 minutes. Repeat with remaining peppers. Peel broiled peppers, discarding skins, and chop coarse.

Cook oil and garlic together in Dutch oven over low heat, stirring constantly, until garlic is foamy, sticky, and straw-colored, 6 to 8 minutes. Stir in onion and ¼ teaspoon salt, increase heat to medium, and cook until softened, about 5 minutes.

Stir in cumin and paprika and cook until fragrant, about 30 seconds. Stir in tomato paste and flour and cook for 1 minute. Slowly whisk in broth, scraping up any browned bits and smoothing out any lumps. Stir in bay leaf and chopped peppers, bring to simmer, and cook until peppers are very tender, 5 to 7 minutes.

Discard bay leaf. Working in batches, process soup in blender until smooth, about 2 minutes. Return soup to clean pot and stir in half-and-half and sherry. Heat soup gently over low heat until hot (do not boil) and adjust consistency with extra hot broth as needed. Stir in remaining 2 tablespoons cilantro and season with salt and pepper to taste. Serve, drizzling individual portions with yogurt mixture.