Cook the bacon and shallot, until the bacon is browned and crisp, remove from the heat and allow to cool, whisk in the mustard and vinegar, and stir very well. Pour dressing over the frisee and toss, well, divide onto 2 plates and top each with a poached egg.
Bring 1 quart of water to a gentle boil with the white vinegar, crack 1 egg into a small bowl, begin stirring the water and drop the egg into the center of the swirl, do the same for the other egg. Poach the eggs for 3-4 minutes, remove from the water and place on top of the dressed frisee.
Place the frisée into a large salad bowl.