Preheat grill to medium-high or preheat oven to 450F.
Cut head of cabbage into bite-sized chunks.
Slice four sausage links into slices about 3/4 inch thick, cut red onion into thick slivers, and cut carrots into slices or half-moon slices just slightly thinner than the sausage.
Lay out four double sheets of foil big enough to hold all the ingredients when it's wrapped into a packet, and spray foil with non-stick spray.
Divide the cabbage, carrots, and onions so one-fourth is on each set of foil sheets, season the vegetables with salt and fresh-ground black pepper to taste and some dried thyme and add about 1 tablespoon of butter.
Then add the slices of sausage on top of the vegetables.
Wrap the inner packet first, then fold over the outer sheet of foil and tightly roll up the ends.
Grill for 20-25 minutes or bake for 30-35 minutes if you're using the oven. Turn once about halfway through.
Approx. Nutrition per serving: 315kcal; 14g NET carbs; 12g protein