Preheat oven to 300 degrees F. In an oven proof, 12-inch skillet, arrange carrots in a single layer. Add broth, honey, butter and seasonings. Heat skillet over medium heat until broth is warmed and butter is melted.
Cover skillet and place in oven. Roast for 30 minutes or until very tender, but not browned. Check liquid after 20 minutes and add a bit more broth or water if the skillet is dry.
With a small paring knife, make a slit at the top of the carrot. Insert parsley sprig if desired.