Heat grill to high heat.
Place the halved potatoes, mini corn cobs, sausage, and shrimp in a large bowl. Sprinkle the rub on top and drizzle with olive oil or melted butter. Toss to evenly coat with the rub.
Take 4 large pieces of foil (about 12 inches by 12-18 inches) and evenly divide the seasoned sausage and vegetable mixture among the pieces of foil, placing the food in the center. Fold up the four sides of each piece of foil and bring two of the opposite sides of foil together, making sure to tuck in the other two sides. Pour a little water, broth or beer into the packets, then crimp together the opening you have created, making sure no air can escape, but leaving room for steam inside the packet.
Place the foil packets on the grill, put the cover down, and cook for about 15 minutes or until the potatoes are fork tender. (Be very careful when opening the packets are the steam escaping will be very hot.) Serve immediately garnished with parsley and with lemon wedges on the side for serving. You can also serve these with some Stubb’s Bar-B-Q sauce on the side for dipping the sausage and veggies in.
To cook in the oven: Preheat oven to 400 degrees. Toss everything but shrimp together in the large bowl and make the packets as the directions state above (including adding the liquid). Place packets on a baking sheet tray and bake for 15 minutes, then carefully open the packets, add in the shrimp, then close them again. Bake for another 5-7 minutes or until the shrimp are pink and firm. Serve with parsley and lemon wedges.