In a bowl, whisk together the olive oil, balsamic vinegar, mustard, and soy sauce to create an emulsified base. Add the brown sugar, minced garlic, lemon pepper, rosemary, smoked paprika, and salt, stirring until the brown sugar dissolves completely and all seasonings are evenly distributed. I like to let this mixture sit for a minute so the herbs can bloom and release their oils—it makes a noticeable difference in the final flavor of the glaze.
Pat the chicken thighs dry with paper towels—this helps the marinade adhere better and allows for better browning later. Place the chicken in a large bowl or zip-top bag and pour the marinade over, ensuring all pieces are well coated. Cover and refrigerate for at least 30 minutes, though marinating for 2-4 hours will develop deeper, more complex flavors. I prefer bone-in thighs because they stay juicier during grilling and absorb the flavors more effectively.
About 15 minutes before grilling, remove the marinated chicken from the refrigerator to allow it to come closer to room temperature—this ensures more even cooking throughout. Meanwhile, preheat your grill to medium-high heat (around 400°F). Once the grill is hot, lightly oil the grates to prevent sticking.
Place the chicken thighs on the grill skin-side down first, letting them cook undisturbed for 5-7 minutes until the skin becomes golden and crispy with light char marks. Flip and cook for another 5-7 minutes on the second side. During the last minute of cooking on each side, brush on extra marinade to build up a glossy, caramelized glaze. Check for doneness by inserting a meat thermometer into the thickest part (without touching bone)—it should read 165°F when done.
Transfer the grilled chicken to a cutting board or serving platter and let rest for 5 minutes—this allows the juices to redistribute throughout the meat, keeping each bite moist and tender. Serve warm, drizzling any pan juices over the top if desired.