Preheat a grill to medium-high heat (375 to 450 degrees). If using the grill basket, place it on the grill while preheating. Or, fold a large piece of aluminum foil in half and prick several holes in it with a fork, then fold up a 1-inch rim around the edge to make a makeshift tray.
Slice off any hard ends of the Brussels sprouts, as needed. Slice them in half lengthwise and place them in a large bowl. Toss with olive oil and kosher salt.
Grill in the grill basket or on the foil tray for 12 to 16 minutes until tender, turning the vegetables a few times to ensure even cooking.
Stir together the balsamic vinegar and honey or maple syrup. When the Brussels sprouts are done, toss them with the sauce. Add a few pinches more salt (since it tends to fall off into the grill), to taste. Serve immediately.