Fill a large skillet with water, bring it to a boil, and add the vinegar and a large pinch of salt. Reduce the heat until the water is just barely bubbling. Crack each egg into a small bowl and carefully slide the egg into the water. Cook until the eggs are set, about 3 1/2 to 4 minutes. Remove the eggs with a slotted spoon and dab the bottom with paper towels to dry them off; set aside and keep warm.

Put the bacon and shallots into a cold skillet with a tablespoon of olive oil and cook over medium heat until the bacon is browned and crisp; be careful not to let it burn. Remove with a slotted spoon, drain on paper towels, and set aside. Meanwhile, get a jar with a tight fitting lid. Add the mustard, remaining 4 tablespoons olive oil, red wine vinegar, and lemon juice. Shake well to combine the ingredients, add the chives, taste, and season with salt and pepper.

Put the frisee into a large bowl and toss it with the dressing the cooked bacon and shallots. To serve, place a large mound of salad onto a plate and top with a poached egg. Garnish with some chives and a drizzle of olive oil.