Preheat your charcoal or gas grill to medium-high heat or about 400℉ (200℃).
Wash and peel your carrots. Slice them lengthwise if they are too big.
Place your prepared carrots in a bowl and add your oil, salt, and pepper to taste. Toss the carrots until evenly coated and set aside.
In a small saucepan, melt the butter over medium heat. Let the butter cook until it starts to foam and turn golden brown, swirling the pan occasionally. Be careful not to let it burn. Once it has a rich golden color and a nutty aroma, take it off the heat and let it cool.
Pass the mixture through a fine mesh sieve to get rid of the specks. Let the brown butter cool slightly.
Wipe down any particles left in the saucepan and pour the drained butter back into the saucepan.
Add in the garlic and thyme. Cook for about 30 seconds or until fragrant, then add the honey and balsamic vinegar. Mix well. Take it off the heat and set aside.
Place your prepared carrots in a bowl, drizzle in your oil, then salt and pepper to taste. Toss until the carrots are evenly coated.
Place the seasoned carrots onto preheated grill grates and grill for 15-20 minutes, depending on the size of your carrots.
Rotate the carrots occasionally until they have grill marks and are nice and tender but not mushy.
Transfer the grilled carrots to a serving plate and drizzle with seasoned browned butter.
Serve with grilled chicken, steak, or fish.