Chrong Chomnei Jrok Oeng Cambodian Style Ginger Lemongrass Baby Backs

Name: Chrong Chomnei Jrok Oeng (Cambodian-Style Ginger Lemongrass Baby Backs)
Ingredients: 2 racks (3 lb.) baby back ribs; 1⁄3 cup packed brown sugar; 1⁄3 cup fish sauce; 1⁄4 cup soy sauce; 2 tbsp. canola oil; 14 cloves garlic, peeled (10 whole, 4 minced); 4 stalks lemongrass, trimmed and thinly sliced; 2 shallots, sliced; 1 (4″-piece) ginger, peeled and sliced; Kosher salt and freshly ground black pepper, to taste; 1⁄4 cup granulated sugar; 2 tbsp. lime juice; 3 fresh red Thai chiles, sliced; 1⁄2 carrot, julienned