Preheat an outdoor grill or grill pan for medium-high heat.
Place the shrimp in a bowl and toss with olive oil and salt and black pepper.
Grill the shrimp on the preheated grill until opaque, 2 minutes per side. Remove from the grill and set aside.
Combine the cabbage, carrot, garlic, 1 tablespoon ginger, teriyaki sauce, and lime juice in a bowl, stir well.
Working with one at a time, wet rice paper with water and lay out on a clean surface. Place a quarter of the cabbage mixture in the center of the paper, top with a quarter of the shrimp. Shape the filling into a log shape and roll the rice paper around the filling, tucking the ends in as you go. Repeat with the remaining rice papers.
Whisk together the peanut butter, teriyaki sauce, sesame oil, hot sauce, garlic, 1 tablespoon ginger, salt and pepper. Slice the rolls in half on an angle, and serve with the peanut sauce on the side.