Martha's recipe is inspired by one from Pastis restaurant in New York City.
Fill a large, deep skillet 2/3 full with water, and bring to a boil. Reduce to a simmer and add white vinegar. Place frisee in a large bowl; set aside.
Cook bacon, stirring occasionally, in a medium skillet over medium-high heat until golden brown, about 6 minutes. Remove bacon, reserving fat, and set aside. Add shallot to pan; cook until translucent, about 2 minutes. Add vinegar; bring to a boil, swirling to combine. Season with salt and pepper and remove from heat. Add bacon.
Break an egg into a small bowl; holding bowl just over simmering vinegar water, gently slide egg into water. Repeat with remaining eggs. Poach 1 to 2 minutes (longer for firm yolks). Transfer to a paper-towel-lined plate.
Return vinaigrette to stove to rewarm if necessary. Pour over frisee and toss gently to combine. Divide evenly among 4 serving plates. Use a slotted spoon to remove poached eggs, and place on the slice of white bread to drain. Top each salad with one egg. Season eggs with salt and pepper. Serve immediately.