Fill a small saucepan with about an inch of water and bring it to a simmer. Place a heatproof bowl over the saucepan, ensuring the bottom of the bowl doesn't touch the water.

Add the egg yolks and lemon juice to the bowl. Whisk continuously until the mixture thickens slightly and becomes pale yellow (about 2–3 minutes).

While whisking, very slowly drizzle in the melted butter. Add it in a thin stream to prevent the sauce from separating. Continue whisking until the sauce is smooth and creamy.

Add a pinch of salt, and season with cayenne or white pepper to taste. If using, mix in the Dijon mustard for added depth.

Serve warm over your favorite dishes, such as poached eggs, steamed vegetables, or grilled fish.