Preheat the oven to 425°F (220°C).
In a small bowl, combine softened unsalted butter, minced garlic, salt, and black pepper to create the herb and garlic butter rub.
Pat the whole chicken dry with paper towels. Gently loosen the skin over the breasts and thighs and spread the herb butter evenly beneath the skin and over the surface of the chicken.
Place the chicken in a large roasting pan or oven-safe dish.
In a separate bowl, toss carrots, baby potatoes, and yellow onions with olive oil, salt, and black pepper until evenly coated.
Arrange the vegetables evenly around the chicken in the roasting pan.
Nestle fresh rosemary and thyme sprigs among the vegetables and on top of the chicken for added aroma.
Roast in the preheated oven for 1 hour 20 minutes, or until the chicken skin is crispy and golden brown and the vegetables are tender and caramelized. An internal temperature of 165°F (74°C) in the thickest part of the thigh confirms doneness.
Remove from oven and let the chicken rest for 10 minutes before carving.
Transfer the whole roasted chicken to a large white oval platter and arrange the roasted vegetables evenly around it for serving.