Preheat your oven to 425°F (220°C). Pat the chicken completely dry with paper towels, inside and out. Place the chicken in the center of a large, rimmed baking sheet.
Drizzle the chicken with olive oil and rub it all over the skin. Season liberally with salt and pepper, including the cavity. If using, stuff the cavity with the halved lemon, smashed garlic cloves, and a few whole thyme sprigs.
In a large bowl, place the peeled and chopped carrots. In a separate, smaller bowl, whisk together the melted butter, honey, minced garlic, and the leaves from a few sprigs of fresh thyme. Season the glaze with a pinch of salt and pepper.
Pour about two-thirds of the honey glaze over the carrots and toss until they are evenly coated. Set aside the remaining one-third of the glaze for later.
Place the chicken in the preheated oven and roast for 30 minutes by itself. This gives the skin a head start on crisping.
After 30 minutes, carefully remove the baking sheet from the oven. Arrange the glazed carrots in a single layer around the chicken.
Return the pan to the oven and continue to roast for another 30-45 minutes, or until a meat thermometer inserted into the thickest part of the thigh registers 165°F (74°C).
During the last 10 minutes of cooking, brush the remaining one-third of the honey glaze all over the top of the chicken to create a lacquered finish.
Carefully transfer the chicken to a cutting board, tent loosely with foil, and let it rest for 10-15 minutes before carving. This allows the juices to redistribute. Toss the carrots in the pan juices before serving.