Preheat the oven to 375°F (190°C).
Rinse the chicken and pat it dry with paper towels.
In a small bowl, mix together olive oil, honey, brown sugar, garlic, thyme, rosemary, cinnamon, allspice, ginger, and star anise.
Rub the mixture all over the chicken, making sure to get some under the skin as well.
Stuff the chicken cavity with the orange and lemon zest, and chopped onion.
Truss the chicken and place it in a roasting pan.
Roast the chicken in the preheated oven for about 1 1/2 hours, or until the internal temperature reaches 165°F (74°C).
Baste the chicken with the melted butter every 20 minutes to keep it moist and promote browning.
Add the chopped carrots to the roasting pan for the last 30 minutes of cooking.
Let the chicken rest for 10-15 minutes before carving and serving.