Place the olive oil in a skillet and turn the heat to medium. Add the bacon and cook slowly until it is crisp all over, 10 minutes or more. Add the shallot and cook for a minute or two longer, until the shallot softens. Keep the bacon warm in the skillet.
Heat a salad bowl by filling it with hot water and letting it sit for a minute. Dry it and toss in the greens. Add the vinegar and mustard to the skillet and bring just to a boil, stirring. Pour the liquid and the bacon over the greens and season to taste; they shouldn’t need much salt.
Divide the salad among 4 plates. Top each portion with a poached egg, sprinkle with croutons if you’re using them, and serve immediately.
