1. Preheat the oven to 200°C (400°F). Put the chicken in a dish, brush it with 2 tablespoons of oil, season with pepper, salt, and sprinkle with half of the thyme. Surround it with unpeeled whole garlic cloves. Cut the parsnips into quarters lengthwise, arrange them on a baking sheet lined with parchment paper, and brush them with 2 teaspoons of olive oil. Bake everything for 20 minutes. Remove the parsnips from the oven, reduce the temperature to 160°C (320°F), and continue cooking the chicken for 40 minutes.
2. Cut the red onions into thick slices. Sauté them in a large sauté pan with 2 tablespoons of olive oil and the remaining thyme. After 5 minutes, add the chicken broth and reduce by half over high heat. Add the harissa, honey, lemon juice, and olives. Remove from heat.
3. Once the chicken is cooked, remove the garlic cloves and squeeze them over the sauté pan to extract the pulp. Mix well, then add the parsnips and simmer for 2 minutes.
4. Serve with flatbread and potatoes.