Using a round pastry cutter or a small cup, cut a small hole in the center of each bread slice large enough to hold an egg inside. For a more rustic look, simply tear the holes. Reserve the centers for another use.  

In a large fry pan over medium heat, melt 2 tablespoons of the butter. Add 2 bread slices and cook, flipping after about 15 seconds. Crack an egg into each “frame” and season with salt and pepper. Cook for about 2 minutes, then gently flip each slice and cook for 2 minutes more. Transfer to a plate. Repeat with the remaining butter, bread slices and eggs.  

Gently toss the lettuce with just enough bacon vinaigrette (recipe follows) to lightly coat the leaves. Season with salt and pepper. Be sure to keep the bacon vinaigrette slightly warm so it will stay liquefied; if it separates, mix it up vigorously before using.

In a bowl, combine the vinegar, shallot and mustard and let stand for about 5 minutes to soften the shallot. Slowly whisk in the bacon fat until incorporated. Add the cheese and season with salt and pepper.

To serve, warm the slices of bread with the eggs slightly before serving.  Stack 2 slices on each plate and place a small pile of salad alongside. Using a vegetable peeler, shave a small amount of cheese over each salad. Top each plate with two slices of bacon, bridging the salad and bread. Sprinkle the chives over the eggs and serve.