Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Spread 1/2 teaspoon butter over the cut-side of each cabbage wedge.
Mix Parmesan cheese, salt, garlic powder, and black pepper together in a bowl; sprinkle over the buttered sides of the cabbage wedges. Wrap a slice of bacon around each wedge and wrap wedges individually in heavy aluminum foil.
Grill cabbage until tender in the middle and the bacon is crisp, turning once, about 40 minutes.