In a small bowl, stir together the mustard and 2 tablespoons of the vinegar into a smooth paste. Cover with plastic wrap and set aside at room temperature to mellow the flavor of the mustard, for at least 6 hours or overnight.
In a medium saucepan, whisk together the yolks, sugar, and salt with the reserved mustard paste. Whisk in the half-and-half. Cook the sauce over medium heat, stirring constantly with a wooden spoon until thickened, about 10 minutes. Do not let the mixture boil at any time. Stir in the remaining 4 tablespoons vinegar and continue to cook for another 10 minutes, stirring, until thickened and creamy. Pour sauce into a bowl. Set the bowl of sauce in a bowl of ice water. Stir the sauce to cool. Serve. Store covered in the refrigerator for up to 2 days. Serve with baked ham, pork or on sandwiches.
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