Combine flour, salt, and pepper in a small saucepan.

Gradually stir in milk until smooth.

Bring to a boil over medium heat, cooking and stirring for 1 minute until thickened.

Reduce heat to low and keep warm, stirring occasionally.

In a double boiler over simmering water, whisk egg yolk, lemon juice, and water constantly.

Continue whisking until the mixture begins to thicken and coats the back of a metal spoon.

Reduce heat to low.

Slowly drizzle in melted butter, whisking constantly to emulsify.

Whisk the milk mixture into the egg yolk and butter mixture.

Serve immediately.