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. Remove the bacon to a paper towel-lined plate to drain.
Reserve about 3 tablespoons of the rendered bacon fat in the pan. Return the pan to medium heat then add the shallots and sauté until tender, stirring occasionally, about 3 minutes.
Remove the pan from heat and add the vinegar. Be careful as the mixture may sputter. Add the mustard, whisking to combine.
Bring the mixture to a boil and let the mixture reduce slightly.
Add the frisée to a medium salad bowl. Pour the hot dressing mixture over the salad and toss to combine, until the frisée has wilted slightly.
Season with freshly ground pepper and serve hot with poached eggs over the top. Garnish with chives (optional). Serve immediately.