Preheat the oven to 375°F (190°C).
Make the herb marinade by combining olive oil, minced garlic, rosemary, thyme, salt, and black pepper.
Rub the marinade all over the rabbit thighs and set aside to marinate while preparing the vegetables.
Chop the vegetables and toss them in a bit of olive oil, salt, and pepper.
Arrange the vegetables in the bottom of a large roasting pan or oven-safe dish.
Nestle the rabbit thighs on top of the vegetables.
Pour the chicken broth or wine evenly over everything and dot with cubes of butter.
Cover with foil and roast for 45 minutes. Then, remove the foil and roast uncovered for another 25–30 minutes, until the rabbit is golden and cooked through.
Optional: Broil for 2–3 minutes at the end for a crisp finish.
Rest for 5 minutes, garnish with parsley, and serve warm.