Preheat a skillet over medium heat. When hot, add bacon and cook slowly until crisp, about 8 to 10 minutes. Remove with a slotted spoon to a plate lined with paper towels, leaving the bacon fat in the pan.

Add the chopped shallot and sauté in the bacon fat until softened, about 3 minutes. Transfer to a bowl and add mustard, vinegar, salt and pepper. While whisking, slowly drizzle in oil until vinaigrette is emulsified. Add reserved bacon and frisée and toss to combine. Divide into 2 plates.

Bring an inch of salted water to a boil in a saucepan. When boiling, reduce the heat so the water is just simmering, barely bubbling. Crack eggs, one at a time, into a ramekin or small shallow bowl. Using a slotted spoon, swirl water and slide the eggs into the water. Cook until whites are set and yolk has filmed over, about 3 to 5 minutes. Using a slotted spoon, remove eggs and place on salad. Garnish eggs with salt and pepper.

Add shaved Gruyére, if using, and serve!