Prepare the chicken: Preheat the oven to 425°F. Remove the chicken from the packaging and discard the giblets, if included. Pat the chicken very dry with paper towels, including the skin around the legs and wings. Let it sit at room temperature for 20–30 minutes while you prepare the remaining ingredients.
Add the lemon butter ingredients to a bowl: Add the olive oil and softened butter to a small bowl. Zest the lemon into the bowl. Cut the lemon in half and squeeze in about 1 tablespoon of lemon juice. Add the garlic and 2 tablespoons of poultry seasoning.
Stir until well combined.
Season the chicken: Carefully loosen the skin over the chicken breasts with your fingers, being careful not to tear it. Spread about half of the lemon butter underneath the skin and over both breasts. Rub the remaining lemon butter over the outside of the chicken. Sprinkle the remaining 2 tablespoons of poultry seasoning evenly over the breast, thighs, legs, wings, and underside.
Arrange the chicken and roast: Slice the remaining lemon and arrange several slices in the bottom of a cast-iron skillet. Place the chicken breast-side up over the lemon slices. Add any remaining lemon pieces to the cavity. If desired, tie the legs together with kitchen twine to help the chicken roast more evenly.
Add the broth: Pour the chicken broth into the skillet around the chicken, taking care not to pour it over the skin. This helps keep the pan drippings from scorching as the chicken roasts.
Roast: Roast at 425°F for 20 minutes. Reduce the oven temperature to 375°F and continue roasting until the skin is deeply golden, the thickest part of the breast reaches 165°F, and the thigh reaches at least 175°F for tender dark meat.
Rest and serve: Remove the skillet from the oven and let the chicken rest for 15–20 minutes before carving. Spoon some of the lemon-butter pan juices over the chicken before serving.
Notes
Cooking time: A 4–5 pound chicken generally takes about 1 hour 10 minutes to 1 hour 30 minutes total. Use the internal temperature rather than the cooking time to determine when the chicken is done.
Check for doneness: The thickest part of the breast should reach 165°F and the inner thigh should reach at least 175°F. Avoid touching the bone with the thermometer.
For crispier skin: Pat the chicken very dry before seasoning. For even better browning, season and refrigerate it uncovered overnight.
Seasoning: The extra salt helps bring out the flavor of the poultry or rotisserie seasoning without adding more herbs.
Rest before carving: Let the chicken rest for 15–20 minutes to help keep the meat juicy.