Combine the brown sugar, soy sauce, garlic, olive oil, paprika, rosemary, thyme, salt, and pepper in a mixing bowl. Mix well until the sugar dissolves and everything is combined into a flavorful marinade.
Place the lamb ribs in a large resealable plastic bag and pour the marinade over them. Seal the bag, making sure the ribs are fully coated. For maximum flavor, refrigerate for at least 2 hours, but overnight is best for a rich taste.
If grilling, preheat it to medium-high heat (around 350°F). For an oven, set it to 350°F. Allow the ribs to sit at room temperature for about 30 minutes before cooking.
Grill the ribs bone-side down for 10–15 minutes per side, basting occasionally with leftover marinade for extra flavor. If roasting, place them on a baking sheet and roast for 1.5 to 2 hours, basting every 30 minutes to achieve that caramelized finish.
Remove the ribs from heat and allow them to rest for 5 minutes to lock in the juices. Slice them into individual servings and garnish with fresh parsley for a pop of color.