In a small bowl, combine the softened unsalted butter, minced garlic, chopped rosemary, chopped thyme, salt, and black pepper. Mix until evenly incorporated and fragrant.
Remove the giblets from the chicken cavity if present, then pat the chicken dry with paper towels to ensure crispy skin. Gently loosen the skin over the breast and thighs without tearing.
Spread about two-thirds of the garlic-butter mixture underneath the skin, smoothing it evenly over the meat. Use the remaining butter to rub all over the outside of the chicken skin.
Stuff the chicken cavity with the halved lemon and quartered onion. Use kitchen twine to tie the legs together and tuck the wing tips under the body for even cooking.
Preheat oven to 425°F (220°C). Place the chicken breast-side up on a rack inside the roasting pan or in an oven-safe skillet. Roast for about 1 hour and 15 minutes, or until the internal temperature reaches 165°F (74°C) in the thickest part of the thigh. Baste halfway through roasting.
Transfer the chicken to a cutting board and cover loosely with foil to rest. Place the roasting pan with drippings on stovetop over medium heat. Add chicken broth, scraping browned bits with a wooden spoon. Simmer 5-7 minutes until sauce thickens. Strain if desired.
Carve the rested chicken into pieces and arrange on a platter. Drizzle pan drippings sauce over the chicken, sprinkle with freshly chopped parsley, and serve immediately.
