The five foundational sauces of classical French cuisine from which all others derive: béchamel (milk + white roux), velouté (white stock + blond roux), espagnole (brown stock + brown roux + tomato), hollandaise (butter + egg yolk emulsion), and tomato sauce. Codified by Escoffier, each spawns dozens of derivative 'daughter' sauces. The system is a framework for understanding how any sauce works: a liquid, a thickening method, and flavouring.
Béchamel: white roux cooked 2-3 minutes (no colour), milk added gradually, simmered 20-30 minutes to cook out raw flour. Velouté: blond roux with white stock (chicken, fish, veal), simmered and skimmed. Espagnole: dark roux, brown stock, mirepoix, tomato — reduced by half over hours. Hollandaise: clarified butter emulsified into warm egg yolks over gentle heat with lemon juice. The system matters because understanding the mother sauce means you can create any derivative: béchamel + cheese = Mornay, velouté + cream + mushroom = supreme.
The temperature trick prevents lumps: hot roux + cold liquid, or cold roux + hot liquid. Hollandaise: if it starts to break, add an ice cube and whisk vigorously — the cold re-emulsifies the butter. Modern kitchens have largely replaced espagnole with demi-glace (equal parts espagnole and brown stock, reduced by half). Understanding these five sauces means you understand every sauce in the Western canon.
Lumpy béchamel from adding milk too fast. Under-cooking the roux — raw flour taste. Over-heating hollandaise — eggs scramble above 75°C. Not skimming velouté and espagnole — impurities make them cloudy. Treating the sauces as recipes rather than frameworks — the value is understanding the principle, not memorising ratios.