Using your hands, combine the turkey with the next 6 ingredients (through egg) in a medium bowl and place in the refrigerator.
Heat the oil in a large pot over medium heat until shimmering. Add the onion, garlic, chili powder and cumin and cook, stirring occasionally, until the onion has softened, about 5 minutes.
Add broth and water, increase heat to high and bring to a simmer.
Add carrots, tomatoes and tomato paste to the broth, stir to combine and return to a simmer.
Reduce heat to medium-low and roll heaping tablespoons of meat into 1-inch balls, wetting your hands as necessary to prevent sticking, and carefully drop meatballs into the soup. Return to a simmer and cover the pot with a lid. Cook for 15 minutes.
Add the zucchini and simmer uncovered until the zucchini is tender, about 10 minutes.
Stir in cheese, hot sauce and oregano.
Serve with cilantro, tortilla chips and a wedge of lime.