In a medium, heavy-bottomed saucepan, combine the onion, vinegar, 1 cup water, and the mushrooms and bring to a boil. Reduce to a simmer and cook until the liquid is reduced by half. Remove from the heat and allow to cool in a large, clean bowl.
Place the cooled mixture into the bowl of a food processor and puree with the mustard and olive oil until emulsified. Pass the mixture through a strainer to remove the mushroom and onion solids, then stir in the black truffles. This can be refrigerated for up to 2 weeks in an airtight container.