Cook the beans:
Wrap the bay leaves, garlic, and thyme in cheesecloth and tie with twine. Put the chickpeas in a large pot and cover with water by 2 inches (about 2 quarts). Add the herb bundle and the salt. Bring to a boil over high heat. Lower the heat to maintain a very gentle simmer, cover, and cook until the chickpeas are tender (try biting into one) but not splitting and falling apart, about 2 hours (check occasionally to be sure the chickpeas aren't boiling and are covered with liquid; add water if needed). Discard the herb bundle. Set aside the chickpeas and their cooking liquid.
Make the soup:
Heat 1-1/2 Tbs. of the oil in a large saucepan over medium-high heat for 30 seconds. Add the onion, carrot, and celery, season with salt, and cook, stirring occasionally, until the vegetables soften and start to brown, about 7 minutes. Add the garlic and cook for 30 seconds, stirring. Add the chickpeas and their cooking liquid (there should be about 4 cups; if not, add more water to equal this amount) and half of the thyme. Season well with salt and pepper. Bring to a boil, reduce the heat to a bare simmer, and cook for 30 minutes so that the chickpeas soften a little more but don’t break up. Working in batches, purée the chickpeas and broth in a blender. Return the puréed soup to the saucepan, stir in the cream, vinegar, and remaining chopped thyme, and keep warm over low heat, stirring occasionally to prevent scorching. Taste for salt, pepper, and vinegar.
Set a large skillet over medium-high heat for 1 minute. Cook the chorizo in the remaining 1-1/2 Tbs. oil until it’s brown and crisp, about 8 minutes; reduce the heat if it starts to burn. With a slotted spoon. transfer half the chorizo to a plate lined with paper towels and stir the rest into the soup. Reserve the cooking oil from the chorizo, if you like.
Laddle the soup into shallow bowls. Sprinkle with the chorizo, scatter with the chives, and drizzle with a bit of the reserved chorizo oil, if you like. Serve immediately.