Preheat your oven to 350°F (175°C). Grease a baking dish or pan with butter or non-stick cooking spray.
Crack the eggs directly into the prepared baking dish, being careful not to break the yolks.
Place the baking dish in a larger pan and pour hot water into the larger pan until it reaches about halfway up the sides of the egg dish. This creates a water bath to ensure even cooking.
Bake for 30 minutes, or until the eggs are set but still soft and creamy. They should have a custard-like texture when done.
Remove the eggs from the oven and let them cool slightly. Then, use a fork to gently break up the eggs into small pieces in the baking dish.
Add the remaining egg salad ingredients - mayonnaise, mustard, celery, onion, herbs, salt and pepper - and stir gently to combine.
Chill the egg salad for at least 30 minutes before serving to allow the flavors to meld.