In a small bowl, thoroughly combine softened butter, minced garlic, chopped rosemary, thyme, parsley, lemon zest, smoked paprika, 1 teaspoon of kosher salt, and cracked black pepper until smooth and fragrant.

Preheat oven to 425°F (220°C). Arrange the halved baby potatoes, carrots, and onion wedges in the bottom of a large roasting pan or 12-inch cast-iron skillet. Pour in the 1/2 cup chicken broth.

Pat the whole chicken completely dry inside and out with paper towels (moisture is the enemy of crispy skin). Generously season the inside cavity with salt and pepper, then stuff with lemon halves, garlic head halves, and fresh herb sprigs.

Gently slide your fingers under the breast and thigh skin to loosen it from the meat without tearing. Spread two-thirds of the garlic herb butter directly underneath the skin over the breast meat. Rub the remaining herb butter and olive oil evenly over the entire exterior skin. Tie legs together with kitchen twine and tuck wing tips behind the back.

Place the chicken breast-side up directly on top of the bed of vegetables. Roast at 425°F (220°C) for 20 minutes to jump-start the sizzling skin.

Reduce oven temperature to 375°F (190°C) and continue roasting for 45 to 55 minutes, basting once or twice with the melted pan juices, until an instant-read meat thermometer inserted into the thickest part of the thigh reads 165°F (74°C) and juices run completely clear.

Transfer chicken to a carving board and rest uncovered for 15 minutes before carving. Spoon the golden pan drippings and roasted vegetables around the carved slices to serve.