Preheat grill to 400 F.

Scrub and wash sweetpotatoes. Cut each into six wedges. (If sweetpotatoes are long, consider cutting wedges in half.) Parboil sweetpotatoes 5 minutes, drain and cool 5 minutes.

Shred cabbage into thin slices.

Toss sweetpotatoes with olive oil and salt and pepper, to taste.

Place sweetpotato wedges on grill perpendicular to grates over direct heat; grill about 3 minutes on each side, or until tender-crisp with grill marks on each side. Remove from grill and set aside.

In zip-top bag or large bowl, toss cabbage with 4 tablespoons poppyseed dressing until coated. Add parsley and tomatoes; toss.

To serve, place sweetpotato wedges on bed of dressed cabbage and drizzle with remaining poppyseed dressing then sprinkle with cheese.

Serve warm or cold.