Shell and devein shrimp and mince garlic. In a bowl stir together garlic, brown sugar, soy sauce, chili powder, lime juice, red pepper flakes, and 2 teaspoons oil and add shrimp, tossing to coat. Marinate shrimp 15 minutes.
Preheat broiler.
Pit and peel avocado and cut into 1-inch pieces. Drain shrimp and arrange on rack of a broiler pan in one layer. Broil shrimp about 4 inches from heat 2 minutes and with tongs turn shrimp over. Broil shrimp 2 minutes more, or until just cooked through, and transfer to another bowl. Add avocado, lemon juice, coriander, remaining 2 teaspoons oil, and salt and pepper to taste and gently toss to coat.
