Place the egg yolk and Dijon mustard in a bowl and whisk until smooth and slightly thickened. Slowly drizzle in the oil while whisking continuously until the mixture emulsifies and becomes thick and creamy. Stir in lemon juice and season to taste.
Bring a pot of water to a boil, then gently lower the eggs into the water. Reduce to a simmer and cook until the eggs are set. Transfer them to an ice bath and allow them to cool before peeling.
Peel the eggs and transfer them to a mixing bowl. Mash them gently with a fork, then add the mayonnaise and mix until combined, keeping a slightly chunky texture.
Stir in chopped chives and season with salt and pepper as needed.
Layer watercress on slices of bread, add a generous portion of egg salad, and top with additional greens and another slice of bread. Serve immediately.