In a mixing bowl, combine 4 tablespoons of softened unsalted butter, 2 tablespoons of olive oil, and 4 minced garlic cloves. Stir in the zest and juice of 1 lemon, along with 1 tablespoon each of chopped fresh rosemary, thyme, and parsley. Season generously with salt and pepper.

Carefully loosen the skin of the whole chicken (3-4 lbs) with your fingers, creating pockets for the marinade. Rub the herb-infused mixture both under and over the skin, ensuring an even coating. Let the chicken marinate in the refrigerator for at least 30 minutes, or up to 2 hours.

Preheat your oven to 375°F (190°C). Gather your vegetables to roast alongside the chicken.

In a large bowl, toss 4 quartered medium potatoes, 3 sliced carrots, and 1 quartered onion with olive oil, salt, and pepper. Pour the coated vegetables into a roasting pan.

Place the marinated chicken on top of the prepared vegetables in the roasting pan. Roast for about 1 hour and 20 minutes, basting halfway through. The chicken is done when golden brown and reaches 165°F (75°C).

Remove the chicken from the oven and allow it to rest for 10-15 minutes before serving.