In a large bowl, toss together the shrimp with the olive oil, Cajun seasoning, brown sugar and minced chipotles in adobo sauce. Mix well to fully coat the shrimp. Cover and refrigerate for 30-60 minutes.
Grilling Method: Preheat an outdoor grill to medium and barbecue shrimp until they curl up and turn pink. These may be threaded on oil-rubbed or water-soaked wooden skewers.
In the meantime prepare the Chipotle Mayonnaise. Serve shrimp with dip.
Baking Method: Preheat oven to 350°F Spread out the marinated shrimp onto a foil-lined baking sheet and season with salt and pepper. Bake until the shrimp curl up and turn pink, about 10-15 minutes. Serve warm or at room temperature with a garnish of lemon or lime wedges.
Sauteeing Method: Preheat a large skillet over medium to medium-high heat. Add about 1/2 tablespoon of oil and once hot add the shrimp, being careful not to overcrowd the pan. Cook about 2 minutes per side.
To Make Chipotle Mayonnaise: Add all of the ingredients in a food processor and blend. Cover and keep refrigerated until ready to use.