In a large nonstick skillet, heat 2 tablespoons of the olive oil. Add the garlic and cook over moderate heat until golden brown, about 2 minutes. Using a slotted spoon, transfer the garlic to a mini processor.
Add the bread cubes to the skillet and cook over moderate heat, stirring, until browned and crisp, 3 minutes; transfer to a plate.
Heat 1 tablespoon of the oil in the skillet. Add the bacon and cook over moderate heat until crisp. Transfer the bacon to a plate; keep warm. Reserve the bacon fat in the skillet.
Add the anchovies, vinegar, mustard and the remaining 1/4 cup of oil to the garlic and process until smooth. Season with salt.
Heat the bacon fat in the skillet. Crack the eggs into the skillet and fry over moderately high heat until over easy, 1 1/2 minutes on one side and 30 seconds on the other side.
In a large bowl, toss the the arugula and croutons with the dressing. Mound the salad on plates and sprinkle with the chives. Top with the bacon and the fried eggs, season with pepper and serve right away.