Combine egg yolk, water, lemon juice, and salt in the bottom of a cup that just barely fits the head of an immersion blender. I recommend a glass measuring cup.
In a small saucepan over high heat, melt butter. Swirl saucepan constantly, until butter is no longer foaming. Transfer butter to a 1 cup measuring cup.
Place immersion blender into the bottom of the cup with the egg mixture. With the blender running, slowly pour hot butter into cup. It will begin to emulsify. Continue pouring until all butter is added and sauce has thickened and is creamy.
Season with salt, if necessary.
If not using immediately, sauce can be transferred to a small lidded pot and kept in a warm place for up to 1 hour before serving.