Place potatoes in a large pot, cover with several inches of water and place on cook top over high heat. Bring to a boil and reduce heat to medium-high. Boil for 10 minutes. Add the corn and boil an additional 4-5 minutes.
Meanwhile, preheat grill to 400 degrees F. Tear off 4 large sheets of foil, folding in half to double-layer. In the center of each piece of foil, divvy out the shrimp, potatoes, corn, and andouille, sprinkling with Old Bay after adding each ingredient to the foil. Drizzle with olive oil and place cubed butter on top of each heap of ingredients. Fold the packets to enclose the contents.
Place the packets on the grill and cook for 8-10 minutes or until shrimp are pink and cooked through. Serve with fresh parsley, if desired.
*Nutrition information based on ½ of butter and oil not being consumed. The ingredients are used for flavor and to create moisture to "steam" the packet contents.