Preheat your oven to 425°F (220°C). Remove the chicken from its packaging and pat it dry with paper towels.
In a medium bowl, combine the softened butter, minced garlic, chopped rosemary, thyme, and parsley. Mix well.
Generously season the inside of the chicken cavity with salt and pepper. Squeeze one half of the lemon inside, and place the other half along with the quartered onion inside the cavity.
Loosen the skin of the chicken from the breast and thighs. Spread half of the garlic herb butter mixture under the skin and the remaining butter all over the outside of the chicken.
Toss the chopped carrots and potatoes with olive oil, salt, and pepper. Place the seasoned chicken on top of the vegetables.
Pour the chicken broth into the bottom of the roasting pan. Roast the chicken for about 1 hour and 15 minutes, or until the internal temperature reaches 165°F (75°C).
Once cooked, let the chicken rest for about 15 minutes before carving and serving with the roasted vegetables.