Combine all dressing ingredients in a food processor; process until mixture is thoroughly blended, about 1 minute; season with salt and pepper and transfer to a bowl.
Combine shrimp, ham, carrot, bell pepper, and onion; set aside. Arrange red leaf lettuce on 6 large plates. Arrange chicory and mixed lettuces on top.
Heat olive oil in a large skillet over high heat until lightly smoking. Add shrimp and vegetable mixture. Sauté, stirring frequently, just until shrimp is cooked through, 3 to 3 1/2 minutes. Add dressing. Toss mixture to combine all ingredients and heat 20 to 30 seconds. Spoon shrimp mixture and dressing evenly over prepared greens. Serve immediately.
Makes 6 servings.