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 saucepan. Add pinch of salt. Add carrots and boil for 7 minutes or until tender and easily pierced with a knife. Drain.
MAKE GLAZE: While carrots are boiling, combine all glaze ingredients in a small bowl.
GRILL CARROTS: Lay carrots on a pan and brush with glaze. (I also spray them with some oil to be extra sure of no sticking to grill). Place on 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.
Make Ahead: The grilled carrots can be made many hours ahead and left on the counter. They can be served at room temperature or warmed for 40-60 seconds in the microwave (or 10 minutes at 350F in the oven).