Preheat the oven to 425 degrees. Toss the carrots, bell peppers, and onion with 1 tablespoon olive oil, 1 tablespoon harissa paste, and half the salt and pepper. Spread on a baking sheet and roast for 25 minutes until the edges brown.
While the vegetables roast, heat the remaining tablespoon of olive oil in a Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 6 minutes.
Stir in the garlic and cook for 1 minute. Add the remaining harissa paste and stir to coat the chicken.
Add the potatoes and chicken broth. Bring to a simmer, then reduce heat to low, cover, and cook for 20 minutes until the potatoes are tender.
Stir the roasted vegetables into the pot. Simmer uncovered for 5 minutes to let the flavors combine. Taste and add the remaining salt and pepper if needed.
Ladle into bowls and sprinkle with chopped parsley before serving.