Preheat your oven to 425°F (220°C). Pat the whole chicken dry with paper towels to help the skin crisp up beautifully. Combine olive oil, minced garlic, chopped rosemary, lemon zest, lemon juice, salt, and pepper in a small bowl.
Rub the olive oil mixture all over the chicken, making sure to get under the skin where possible for maximum flavor infusion. Season the cavity with salt and pepper. Optionally, tuck in a few rosemary sprigs or lemon wedges inside for added aroma.
Place the chicken breast-side up in your roasting pan or oven-safe skillet. Roast uncovered for about 1 hour to 1 hour and 15 minutes, until the internal temperature reaches 165°F (74°C) in the thickest part of the thigh. Baste occasionally with the pan juices to keep the meat moist.
Remove the chicken from the oven and tent it loosely with aluminum foil. Let it rest for 10-15 minutes before carving to allow the juices to redistribute.
While the chicken rests, place the roasting pan on the stovetop over medium heat. Add the chicken broth and scrape up browned bits from the pan. Let simmer and reduce slightly, then whisk in the butter until the sauce is smooth and glossy. Adjust seasoning as needed.
Carve the chicken and serve drizzled with the warm rosemary-garlic pan sauce. Pair with your favorite sides like roasted vegetables or mashed potatoes.
