In a large mixing bowl, combine the chopped Yukon gold potatoes, large carrots, medium onion, half of the cloves of garlic, and fresh rosemary. Drizzle generously with olive oil, then season with salt and pepper to taste. Toss everything thoroughly to ensure the vegetables are well-coated. Set aside as you prepare the chicken.

Preheat your oven to 425˚F (220˚C). Remove the giblets from the whole chicken and pat it dry inside and out with paper towels. Season the cavity with salt and pepper, then stuff it with the remaining garlic cloves, lemon halves, and rosemary.

Melt some unsalted butter in a small saucepan or microwave. Brush the melted butter generously over the exterior of the chicken, making sure to cover all areas for a golden finish. Sprinkle salt and pepper over the skin.

Using kitchen twine, tie the chicken legs together to ensure even cooking, and tuck the wings underneath the body. In a large roasting pan, arrange the seasoned vegetables around the chicken.

Place the roasting pan in the preheated oven and bake uncovered for 80-90 minutes. Check the internal temperature to ensure it reaches 165˚F (74˚C). Juices should run clear when pierced.

Once done, carefully transfer the roasted chicken to a platter. Tent it with aluminum foil and let it rest for at least 15 minutes before slicing.