Melt the butter in a medium saucepan over medium-low heat. Add the shallot; cook 1 minute. Stir in the sliced carrots and the chicken stock. Cook, covered, stirring occasionally, until just tender, about 12 to 15 minutes.
Add the honey and nutmeg. Raise the heat slightly, and cook, uncovered, stirring constantly, until the liquid becomes syrupy. Remove from the heat; toss in the chopped parsley.