Melt butter in bowl of a double boiler set over medium heat.
Whisking vigorously, gradually beat in eggs.
Whisk in sugar and cook, whisking constantly, until completely dissolved, about 1 minute.
Whisk in tomato soup, mustard, vinegar and water. Continue cooking, whisking constantly, until slightly thickened, 7–10 minutes.
Serve hot or cold with ham.
Tomato Soup: it’s important that you use condensed tomato soup, such as Campbell’s. Don’t use a ready-to-eat canned soup like Progresso.To prepare a double boiler: set a glass bowl over a saucepan partially filled with water. The water should not touch the bottom of the bowl. Place the saucepan over medium heat on the stovetop and bring the water to a simmer. Use as directed in the recipe.Store mustard sauce in an airtight glass container in the refrigerator for up to 1 week.