Preheat grill or grill pan to medium-high.
Place carrots and thyme in a mixing bowl and toss together with oil until all carrots are well coated. Season with salt and pepper.
In a small mixing bowl combine the remaining ingredients and whisk together until fully incorporated and sugar is mostly dissolved.
Once grill is hot, spread carrots onto grill or grill pan, in a single layer, and grill for 4 to 5 minutes.
Brush with balsamic butter and flip. Grill for an additional 3 to 4 minutes, brushing carrots with the glaze every 2 minutes.
Once carrots have softened brush with butter mixture and season with salt and pepper.
Drizzle with any remaining balsamic butter, top with citrus zest and adjust seasonings. Serve.