Melt the butter in a small saucepan over medium-low heat.
In a blender or in a large measuring cup with an immersion blender, combine the egg yolks, lemon juice, mustard, and salt.
With the blender running, slowly stream in the warm melted butter, starting with a few drops at a time and gradually increasing the stream as the sauce starts to emulsify.
Once all of the butter has been added, you can stream in hot water, a tablespoon at a time, if you desire a thinner hollandaise.
Taste for seasoning, adding additional lemon juice or salt if desired.
To assemble:
Poach the eggs (see notes). Set aside.
Split the English muffins, toasting each of the halves.
Top each English muffin half with any of your desired optional additions – a slice of Canadian bacon is considered traditional, but feel free to use anything you like. Top with a poached egg; season lightly with salt and pepper.
Spoon the fresh hollandaise over each egg. Garnish with a sprinkle of smoked paprika and a sprig of dill, if desired. Serve immediately.
Notes
Learn how to poach eggs.For a bit of heat, add a pinch of cayenne pepper or a few dashes of hot sauce to your hollandaise.In addition to thinning out thick hollandaise, hot water can be used to revive a broken hollandaise. Gradually add hot water, 1 tablespoon at a time, until the broken sauce comes back together.Hollandaise can be stored in an airtight container in the refrigerator for up to a day. Reheat using a double boiler over very low heat, stirring constantly. Remove the sauce from the heat as soon as it is warm. Use a few drops of hot water to bring the sauce back together if it splits.