Cook the bacon in a medium skillet over medium heat, stirring occasionally, until crisp. Using a slotted spoon, transfer the bacon to a paper towel. Pull the skillet from the heat (leave drippings in the skillet) and stir in 1 12 tablespoons cider vinegar, scraping up any browned bits clinging to the skillet. Pour the mixture into a large bowl and whisk in mustard, salt and pepper to taste, and olive oil.
Fill a nonstick skillet with about 2 inches of water and bring it to the barest simmer over medium heat; add the remaining 1 tablespoon vinegar. Crack the eggs, slipping them gently into the water, and cook until the whites are set but the yolks are still runny, about 4 minutes.
While the eggs poach, toss the greens with the vinaigrette and bits of bacon. Divide the salad among 4 plates or shallow bowls. Using a slotted spoon, gently scoop the eggs from the water, blot dry with a paper towel, and place 2 of them on top of each salad. Add bread to each plate and serve.