Warm up the olive oil in a heavy, large pot suitable for making soup, over medium-high heat. Add the onions, leek, shallots, chili, celery and carrot, and sauté until soft, about 10 minutes.
Add the broth and bring to a simmer. Add the potatoes, fresh thyme, salt, pepper, and rice. Add the bones from the chicken that the cooked breast meat was removed from. Stir in the mashed avocado and lime juice. Simmer for 15 minutes.
Add the Pecorino cheese and roasted chicken, and simmer for 5 minutes longer. Stir in the sherry.
Serve piping hot in soup bowls with a salad and hunk of crusty bread on the side.