Combine dried peas, bacon, thyme, tomatoes, garlic, and chiles in a large pot. Season with salt and black pepper and pour chicken broth over top. Place over medium-low heat and simmer for 1 hour, until peas are tender.

Drain cooked pea mixture, reserving the cooking liquid and discarding the thyme. Remove bacon slices, tomatoes, garlic, and chiles from the cooked peas; set aside. (reserve chiles for garnish.) Cut up bacon slices and fold back into the peas with green onion, cilantro, and lemon juice. Place the cooking liquid, the tomatoes, and the garlic in a blender and puree. Dress the peas with the puree and give it a final season with salt and black pepper. Serve with a drizzle of oil. Garnish with reserved chiles and the cilantro sprigs.