Heat 1 tablespoon oil in a 5-quart soup pot over medium-high heat. Add half the chicken pieces in an even layer and cook until browned, about 1 to 2 minutes per side. Use a slotted spoon to transfer the browned chicken to a bowl and set aside. Brown the remaining chicken the same way and remove it from the pot.
Turn the heat down to medium and add the squash and onion to the pot. Cover and cook 4 minutes, stirring occasionally. Add the garlic and cook 1 minute more, stirring constantly.
Add the chicken stock, pumpkin puree, harissa, salt, and browned chicken along with any juices that have accumulated. Bring the soup up to a boil, and then cover the pot, turn the heat down to simmer, and cook until the squash is tender and the chicken is fully cooked, about 20 minutes, adding the figs after 10 minutes.
Taste and add more salt and/or harissa paste as desired. Serve with lemon wedges to squeeze on top, or let the flavors marry overnight and reheat to serve the next day when it’s even better.