Preheat your oven to 425°F (218°C) and pat the chicken completely dry with paper towels to ensure the skin gets crispy.
Cut the potatoes into halves, slice the carrots into thick rounds, and wedge the onion, then toss them in a large roasting pan with 1 tablespoon of olive oil and a pinch of salt.
Mince the fresh rosemary and thyme, then combine them in a small bowl with the softened ghee, remaining olive oil, salt, and pepper.
Stuff the chicken cavity with the halved lemon and the head of garlic (sliced in half crosswise) to infuse the meat with moisture and aromatics.
Rub the herb-ghee mixture all over the chicken, including under the skin of the breasts, then place the chicken on top of the vegetables in the roasting pan.
Roast for 60 to 75 minutes, or until the internal temperature reaches 165°F (74°C) and the juices run clear.
Remove from the oven and let the chicken rest for at least 15 minutes before carving to allow the savory juices to redistribute.