Preheat the oven to 425 degrees and position a rack in the lower third of the oven. Mix the butter with minced rosemary, 3 cloves of minced garlic, lemon zest, salt, and pepper. Adjust seasoning as needed.

Pat the chicken dry, then gently pull up the skin and rub half of the butter mixture underneath the skin. Rub the remaining half of the butter mixture over the chicken, then sprinkle with salt and pepper.

Generously season the cavity of the chicken with salt and pepper then stuff with 2 lemon halves, 1/2 head of garlic, 2-3 quarters of onion and 2 rosemary sprigs. Tie legs with cooking twine and tuck the wings under bird.

Place chicken in a roasting pan or high-sided large skillet breast-side-up with the remaining onion, garlic, lemons, and herbs, then add the chicken broth. Roast for 1 hour or until the breast is firm and the chicken is turning golden brown. If the chicken is turning too dark, gently cover with a loose piece of foil and roast for about 20 minutes longer, until an instant-read thermometer inserted in the inner thigh registers 165 degrees and juices are running clear.

Transfer the bird to a cutting board and tent with foil. Remove aromatics and vegetables from the cavity, carve the chicken and serve.