While the carrots are smoking, whisk the honey and balsamic vinegar together well in a mixing bowl and set aside.
After the carrots have smoked for 90 minutes, take them off and move them to a glass Pyrex baking dish or baking tray and turn the temperature of your grill or smoker up to 350°F.
Pour the honey balsamic mixture on the carrots and stir well to coat all sides. Spread back out into the baking dish.
Add three 1 tablespoon pieces of salted butter to the top of the carrots.
Once the grill or smoker is up to 350*F, place the baking dish of carrots, glaze and butter back in the grill or smoker.
Monitor the carrots for about 15-20 minutes as the butter melts and the glaze caramelizes. Be careful not to burn the glaze or the carrots.
Check for doneness by piercing a carrot with a knife or fork. It should pass through fairly easily but not be mushy when they are finished.
Remove the tray of carrots from the grill or smoker using oven safe BBQ gloves and place somewhere to cool for 5-10 minutes before serving.
Stir one last time to incorporate the butter and glaze and serve warm. Add more salt and pepper as needed.