Steps
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1Heat gas or charcoal grill. Cut 4 (18x12-inch) sheets of heavy-duty foil. Place ham piece in center of each. Top each evenly with potatoes and vegetable mixture. Bring up foil sides so edges meet. Seal edges, making tight 1/2-inch fold; fold again, allowing space on sides for heat circulation and expansion.
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2Place packets, seam side up, on grill. Cover grill; cook over medium heat 18 to 23 minutes, rearranging packets several times during cooking, until potatoes and vegetables are tender.
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3To serve, carefully open packets to allow steam to escape. Sprinkle each with cheese; close packets and let stand until cheese is melted, 1 to 2 minutes.