You will need 4 pieces of aluminum foil, each about 2 feet long. Preheat your grill to 325-350°F (or medium heat).
Cut the head of cabbage in half and then one of the halves into quarters (save the other half for another use). Cut each quarter into approximately 1-inch chunks and place onto the center of each sheet of aluminum foil.
Dice the shallot and evenly distribute it over the 4 piles of cabbage. Mince the garlic and add that evenly to each packet, as well.
Cut the potatoes into bite size pieces and divide them evenly among the packets. Season each packet with salt and pepper.
Slice each sausage link into 8 pieces. Scatter them on top of the packets. Top each packet with 1 Tablespoon of the butter.
Fold the long edges of the foil over the ingredients, and tightly roll up the sides.
Place the foil packets on the grill and cook for about 15 minutes.
After 15 minutes, open a packet and check the potatoes for fork tenderness. If needed, heat an addition 2-5 minutes, but watch closely as to not burn the cabbage.
See notes section for how to bake in the oven.