Cut the tops off the beets, leaving 1 inch of stems attached. Place the beets in a pot o cold water to cover, bring to a boil, reduce heat, and boil until the beets can be pierced easily with a sharp knife, 45-60 minutes depending upon their size.
Meanwhile, whisk together the mustard and vinegar in a bowl, then whisk in the olive oil in a steady stream until the sauce is smooth and creamy.
When the beets are done, drain them and submerge them in cold water until they are cool enough to handle. When cooled, cut off the roots and tops, and slip the skins off. Slice the warm beets into the mustard sauce. Mix well, cover, and let marinate in the fridge at least 24 hours. Season before serving, if needed.