Whisk together the vinegar, water, sugar, flour, mustard, salt, and pepper in a small pot until smooth. Place over moderate heat and bring to a simmer, whisking constantly. Add the cream and butter, whisking until the butter melts and is incorporated. Stir a little of the hot mixture into the eggs, then transfer the egg mixture to the pot. Reduce the heat to low and continue whisking until the sauce thickens-do not boil. Transfer to a bowl and cool to room temperature. Toss with the shredded cabbage and carrots and refrigerate for at least 2 hours before serving. Serves 8 to 12.
