Start by preheating your oven to 475°F. While the oven is heating, line a large, rimmed baking sheet with either foil or parchment paper to make cleanup easier. Set the prepared sheet aside until you're ready to add the chicken.
Place the chicken thighs and drumsticks onto the prepared baking sheet. Generously season all sides of the chicken with salt and black pepper. Use your hands to thoroughly rub the seasoning into the chicken, ensuring it is evenly distributed.
In a small bowl or measuring cup, whisk together the honey, balsamic vinegar, and dried thyme until well combined. This sweet and tangy glaze will add a delicious flavor to the chicken. I like to make sure I really blend the thyme in well for an even distribution in every bite.
Drizzle a small amount of the honey balsamic glaze from Step 3 over each piece of seasoned chicken on the baking sheet. Use a brush to evenly coat the chicken with the glaze. Place the chicken in the preheated oven and roast for 20 to 25 minutes, or until fully cooked. Halfway through roasting and again near the end, brush the chicken with more glaze to build up a flavorful, sticky coating. Serve immediately for the best taste and texture.