Heat oven to 375°F and spray a shallow, rimmed baking dish/pan (just large enough to hold the carrotwith cooking spray.
The carrots should be close in size for baking. If they are on the thin size, use as is. If they are on the large size, cut them in half lengthwise. Just try to have the carrots as close to the same size as possible.
In a medium, stainless, heavy-bottom skillet, cook butter over medium heat. Once the butter comes to a boil, swirl or stir the butter every 15 seconds. When the butter just begins to darken, watch closely and stir more often. Butter has turned to “browned-butter” when it has a nutty fragrance and the milk fats, on the bottom of the pan, turn dark golden brown.
Add salt, black pepper, brown sugar, vinegar and red pepper flakes. Bring to a boil, reduce the heat to medium-low and simmer until the mixture has reduced and thickened a little, about 3-4 minutes.
Place the carrots side-by-side in the prepared pan and pour the butter/vinegar sauce over the top.
Bake carrots at 375°F for 15 minutes. Rotate the pan and turn the carrots over. Glaze with the pan juices, and bake another 15-20 minutes or until the carrots have softened and glaze has caramelized.
Transfer the carrots from the stove, re-glaze with pan juices and lightly sprinkle with salt and chopped chives or thyme.