Remove the majority of the stalks from the parsley and finely cut it.
In a medium saucepan over medium to low heat, melt the butter. When the butter has melted, stir in the flour.
Stir in the flour until it forms a thick paste or roux. Then cook for a few minutes, stirring constantly. Thoroughly cook the roux. Otherwise, the sauce may have a floury flavor.
Begin gradually adding the milk, a little at a time, stirring thoroughly after each addition to form a smooth paste. You can add more milk when the mixture thickens into a sauce.
Simmer for a few minutes to allow the sauce to thicken. Continue to stir constantly. To ensure uniform consistency and avoid burning, scrape the edges and bottom of the pan where the sauce will thicken faster.
Season with pepper and salt to taste and stir in the finely cut parsley. If you’re using mustard, lemon, or cream, add them now.
In the pan, the sauce will remain heated for 15-20 minutes. If you need to leave it for a longer period of time, add a circle of buttered parchment or greaseproof paper on top to prevent skin from developing.
Notes
Making sure the roux (flour and butter) is cooked thoroughly is essential to avoiding a flour flavor in the finished sauce.
As a precaution against lumps forming, add the milk very gradually, a few drops at a time, while stirring constantly.
Adding extra milk and simmering the sauce should fix the problem if it’s too thick.
The sauce can be thickened by adding a slurry or paste made from a teaspoon of cornflour (cornstarch) and a little milk, which should be added to the sauce, stirred in and cooked for a few minutes longer if necessary. And if it doesn’t work, try again.
There isn’t enough flavor for dried parsley to work in this sauce. In my opinion, freezing parsley is the best option. Drying it out ruins it.
In a jar of water in the fridge, freshly cut parsley will keep for up to a week. A plastic bag placed loosely over it might help it survive even longer. This will prevent the leaves from losing their moisture. Similarly, it may be frozen.