Heat grill to medium high 425-450F spray grates with oil or oil grates with a paper towel dipped in oil.
Parboil carrots: if using medium or large carrots, cut the carrots lengthwise in halves or quarters to about 1/2-3/4 inch thickness. Bring 1-2 inches of water to boil in large sauce pan.Add carrots and boil for 7 minutes or until tender easily pierced with a knife. Drain. While carrots are boiling, combine all glaze ingredients in a small bowl.
Lay carrots on a pan and brush with glaze ( also spray them with some oil to be extra sure o no sticking to grill) place on the grill. Cover grill for 5-6 minutes total, turning and glazing a couple of times.
Serve: Transfer to plate drizzle leftover glaze. Garnish with thyme green onions or chives. Serve
