Peel and butterfly the shrimp, keeping the tail fins intact.
Peel the ginger and garlic. Finely chop the ginger, garlic, and red pepper together. Clean and wash the lamb's lettuce.
Heat 4 tablespoons of light sesame oil in a saucepan over medium heat. Add the ginger, garlic, and red pepper, and sauté for 2 minutes. Stir in the brown sugar and cook for 1 minute until melted. Remove from heat and stir in 4 tablespoons of light soy sauce and 5 tablespoons of lime juice.
Place the shrimp in a container. Pour the hot marinade over the shrimp, reserving 2 tablespoons for the salad dressing later. Cover and refrigerate overnight.
Heat 2 tablespoons of vegetable oil in a grill pan over medium-high heat until it shimmers. Add the marinated shrimp and grill for 3–4 minutes, turning every 30 seconds, until golden brown and cooked through.
In a small bowl, whisk together the reserved 2 tablespoons of marinade, 2 tablespoons of walnut oil, 1 tablespoon of lime juice, and salt and pepper to taste. Toss the lamb's lettuce with this dressing.
Arrange the dressed lamb's lettuce on plates and top with the grilled shrimp.
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