It is a classic French salad, which may seem strange because it is actually served hot, but the oil actually just helps to make the tough leaves of frisée tender.
Bring a pot of water to a bare simmer. Create a clockwise swirling motion with a ladle to create a whirlpool then carefully crack each egg individually into the pot, being careful to space them out. Cook until the whites are just set and the yolk is runny, about 3 minutes. Use a slotted spoon to remove the eggs and set them aside on a plate.
Add the bacon to a medium sauté pan over medium heat, and cook, until the fat has rendered and the bacon is crispy, about 5 minutes.
If there is an excessive amount of oil left in the pan, pour some out, reserving about 3 tablespoons of it in the pan. Add the shallots to the hot oil and sauté until tender, about 3 minutes.
Add the frisée to a medium salad bowl and pour the hot fat and the crispy bacon over the salad. Toss to combine and continue to toss until the leaves are slightly wilted, about a minute.
Return the pan used to cook the bacon to medium heat, and add the vinegar to the hot pan. Be careful as the mixture may sputter. Add the mustard, whisking to combine.
Bring the mixture to a boil and let the mixture reduce to about half. Pour the vinegar mixture over the salad and toss to combine.
Season with freshly ground pepper and serve hot with poached eggs over the top. Garnish with chives. Serve immediately.