Combine all of the marinade ingredients in a blender until smooth.
Cover the shrimp in the marinade in a bowl or zip-top bag and marinate in the fridge overnight, or for at least 4 hours.
Preheat the oven to 350°F. Arrange the shrimp on a baking sheet, discarding the marinade. Roast for 6-8 minutes, until cooked through and bright pink.
Combine all of the dressing ingredients in a blender or with a whisk until smooth. Adjust the seasoning.
In a large bowl, toss the salad ingredients together. Add the shrimp and dressing, toss well and serve.