Place the shredded cabbage, grated carrot, and diced onion in a large heat-proof mixing bowl and toss to combine.
In a small saucepan over medium-high heat, combine the apple cider vinegar, sugar, vegetable oil, dry mustard, celery seed, salt, and pepper.
Bring the dressing mixture to a rolling boil, stirring constantly until the sugar has fully dissolved.
Immediately pour the hot dressing over the cabbage mixture.
Toss the vegetables thoroughly with tongs to ensure all components are evenly coated.
Allow the mixture to cool to room temperature, then cover and refrigerate for at least 2 hours before serving to allow the flavors to marinate.