Cover the eggs with water in a small saucepan, bring to a boil, then cover, remove from the heat and stand for 10 minutes.
Transfer the eggs to ice water for 5 minutes, peel them and cut each into quarters.
Whisk the mayonnaise, vinegar, mustard, honey, salt and pepper until the dressing is smooth and pourable.
Toss the romaine, iceberg and tomatoes with two-thirds of the dressing in a broad bowl.
Scatter the cheddar and croutons over the dressed greens and arrange the egg quarters on top.
Drizzle with the remaining dressing immediately before serving.