Mix brown sugar, paprika, chili powder, salt, and garlic powder in a medium bowl.

Cut ribs into equal portions. Generously rub spice mixture onto all surfaces of ribs; place ribs in a single layer in a glass baking dish. Cover and refrigerate for 30 minutes to 1 hour.

Preheat grill to medium indirect heat, 375 to 400 degrees F (190 to 200 degrees C).

Center one portion ribs on a 12x18-inch sheet of heavy-duty aluminum foil; add 2 ice cubes. Bring up the foil sides, then double-fold the top and ends to seal the packet, leaving room for heat circulation inside. Repeat to make 3 more packets.

Arrange packets over indirect heat on the preheated grill. Cover and cook until tender, 1 1/2 to 2 hours.

Uncover the grill. Keeping the foil packets on the grill, open them carefully by cutting along the top folds with a sharp knife, allowing steam to escape; then proceed to open packets fully.

Brush ribs with about 1/2 cup barbecue sauce.

Move packets over direct heat, cover, and continue grilling, turning once, until ribs are browned and crisp, about 5 minutes more.