Preheat oven to 425°F (220°C). In a small bowl, combine softened butter, minced garlic, chopped rosemary, thyme, sage, lemon zest, smoked paprika, salt, and pepper until uniform and fragrant.

CRITICAL CHEF STEP: Thoroughly pat the entire chicken dry inside and out with paper towels. Removing surface moisture is the #1 secret to achieving crackling crisp skin rather than steamed skin!

Season the internal cavity generously with salt and pepper. Stuff the cavity with the lemon halves, garlic head halves, and fresh herb sprigs.

Gently slide your fingers between the chicken breast meat and skin to create a pocket. Spread two-thirds of the garlic herb butter directly onto the breast meat under the skin. Rub the remaining butter over the outside of the chicken, legs, and wings. Tie the drumsticks together with kitchen twine and tuck the wing tips back.

In a large roasting pan or 12-inch cast iron skillet, toss potatoes, carrots, and onions with olive oil, salt, and pepper. Nest the chicken breast-side up directly on top of the vegetables.

Roast at 425°F (220°C) for 20 minutes to sear the skin, then reduce heat to 375°F (190°C). Roast for an additional 50 to 55 minutes, basting once with pan juices at the 45-minute mark, until an instant-read thermometer inserted into the thickest part of the thigh reads 165°F (74°C).

Transfer chicken to a carving board and rest loosely tented with foil for 15 minutes before carving. Pour bone broth into the pan to deglaze those caramelized drippings, simmer for 3 minutes, and serve as rich natural pan jus!