Preheat your oven to 400°F (200°C). Line a large rimmed baking sheet with foil or parchment for easier cleanup, then set a wire rack on top if you have one. If not using a rack, lightly grease the foil.
Place the chicken hindquarters on a cutting board or paper towels and pat very dry on all sides, especially the skin. Trim any large excess pieces of fat if needed.
In a small bowl, mix together the salt, pepper, garlic powder, onion powder, smoked paprika, dried thyme, dried rosemary, and brown sugar (if using). Drizzle the olive oil over the chicken and rub it all over. Gently loosen the skin from the meat with your fingers and rub some of the spice mixture directly onto the meat under the skin. Sprinkle the remaining seasoning evenly over the outside of the chicken.
Spread the sliced onion and smashed garlic (if using) over the prepared baking sheet. Lay the seasoned chicken hindquarters on top, skin-side up, leaving a little space between each piece so the heat can circulate.
In a small cup, stir together the lemon juice and Worcestershire sauce (or soy sauce). Brush or spoon this mixture evenly over the chicken skin.
Place the pan on the center rack and bake for 40–50 minutes, rotating the pan halfway through for even browning. The chicken is done when an instant-read thermometer inserted into the thickest part of the meat (not touching the bone) reads 175–185°F (80–85°C).
If the chicken is cooked through but you want extra-crispy skin, turn the oven to broil and cook for 2–4 minutes, watching closely so the skin does not burn.
Transfer the baked chicken hindquarters to a platter and let rest for 5–10 minutes to allow the juices to redistribute. Spoon some of the pan drippings over the top if desired and serve with your favorite sides.