5 slices thick-cut bacon, cut into 1⁄2"-strips
1 tbsp. fresh lemon juice
2 tsp. Dijon mustard
1 small shallot, minced
Kosher salt and freshly ground black pepper, to taste
2 tbsp. extra virgin olive oil
8 oz. frisée, torn into bite-size pieces
1 tbsp. white wine vinegar
Boil bacon and 1 cup water in a 12" skillet. Reduce heat to medium-high; cook until water is evaporated and bacon is crisp, 35–40 minutes. Using a slotted spoon, transfer bacon to paper towels to drain. Transfer 3 tbsp. bacon fat to a large bowl. Add lemon juice, mustard, shallot, salt, and pepper. While whisking, slowly drizzle in oil until vinaigrette is emulsified. Add reserved bacon and the frisée; toss and divide between 4 plates.
Boil a 4-quart saucepan of water; add vinegar, reduce heat to medium, and, using a slotted spoon, swirl water. Crack eggs, one at a time, into aramekin, and slide into water; cook until whites are set, about 2 minutes. Using a slotted spoon, divide eggs between plates; garnish with more black pepper.