First Step: Prepare Butter and Ingredients
Melt 1/2 cup unsalted butter until hot, either by microwaving for about one minute or gently on the stove over medium-low heat. Meanwhile, separate 3 large egg yolks carefully, ensuring no egg white remains, as it can affect emulsification.

Second Step: Whisk Egg Yolks and Lemon Juice
In a heatproof bowl or the container of a high-powered blender, combine the egg yolks with 1 tablespoon fresh lemon juice, 1 teaspoon Dijon mustard, 1/4 teaspoon salt, and a pinch of cayenne pepper. Whisk or blend for 5 to 15 seconds until the mixture is frothy and lightened in color.

Third Step: Emulsify Butter into Egg Mixture
With the blender running on medium-high or using a whisk in a bowl over a double boiler, slowly drizzle the hot melted butter into the egg yolk mixture, blending continuously. This process emulsifies the butter with the yolks, producing a smooth, creamy hollandaise sauce.

Fourth Step: Adjust Sauce Consistency and Seasoning
If the sauce becomes too thick or begins to split, gradually add one to two tablespoons of hot water while whisking or blending to smooth and loosen the sauce. Taste and adjust the salt, lemon juice, or cayenne pepper as needed for balance.

Final Step: Serve Warm
Remove the hollandaise sauce from heat if using the stovetop method, or stop blending if using a blender. Serve immediately while warm, drizzling over eggs Benedict, steamed vegetables, grilled fish, or your favorite dishes. To keep it warm for brief periods, place the sauce bowl over very low heat and stir occasionally to prevent separation.