Melt the butter in a heavy-bottomed saucepan. Stir in the flour to make a roux, stirring constantly, until the paste cooks and bubbles a bit, but is not brown, about 2minutes.

Add the hot milk, continuing to stir as the sauce thickens.  Bring it to a boil. Add salt and pepper to taste, lower the heat, and cook, stirring for 2 to 3minutes more.

Remove from the heat.  Mix in the mashed anchovies.

To cool this sauce for later use, cover it with wax paper or pour a film of milk over it