Heat a heavy-bottomed Dutch oven or soup pot to medium heat and add the oil. Put the chicken wings and breasts in skin-side down and cook without moving until golden brown, 6 to 8 minutes. Set aside the chicken.
Add the carrots, celery and shallots. Saute until the shallots are translucent, about 10 minutes, stirring all the while. Deglaze with the dry sherry and scrape up any bits off the bottom. Add the stock, fresh thyme and bay leaf, return the chicken to the pot and bring to a low simmer; simmer until the chicken is cooked through, about 20 minutes. Set aside the chicken to cool on a plate.
Meanwhile, bring a large pot of salted water to a boil.
Shred the chicken breasts and whatever can be salvaged from the wings and pour any reserved juices back into the soup pot. Add in the chicken and adjust the seasoning if necessary. Just before serving, add in the lemon zest and juice to taste.
Cook the tortellini in the salted water just until al dente.
Put some tortellini in each individual bowl, then ladle the soup over. Serve immediately to retain the al dente quality of the tortellini. Garnish with a wedge of lemon and fresh parsley.