Arrange the Carrots: Spread the carrot pieces in an even layer across a sauté pan.
Add Water: Place the pan over medium-high heat and pour in enough water to just barely cover the tops of the carrots.
Season: Sprinkle the kosher salt evenly over the carrots and water.
Simmer the Carrots: Bring the water to a simmer, then continue simmering while gently shaking the pan every few minutes.
Cook Until Tender: Continue cooking for 10–12 minutes, or until the water has cooked off and the carrots are tender. If the water evaporates before the carrots are tender, add a small amount of additional water and continue simmering until they reach the desired tenderness. Prepare the Glaze: Whisk the honey, Dijon mustard, red or white wine vinegar, and olive oil together until combined.
Glaze the Carrots: Pour the honey mustard mixture over the cooked carrots and stir for 1 minute, allowing the sauce to coat the carrots evenly.
Serve Warm: Transfer the glazed carrots to a serving dish and serve while warm.