Heat oil in a large nonstick skillet over medium-high heat. Add garlic and ginger; cook, stirring, until fragrant, about 30 seconds.
Add shrimp and cook, stirring, until pink and beginning to curl, about 2 minutes.
Add soy sauce, sambal oelek (or Sriracha) and honey. Cook, stirring, until the shrimp is opaque and cooked through, about 1 minute more.
Remove from heat and stir in carrots, snow peas, basil and mint. Serve the shrimp mixture in lettuce leaves.
