Wash and peel the russet potatoes. Cut them into 1/3–1/2 inch (8–12 mm) sticks for classic fries. Place cut fries in a large bowl of cold water and soak for at least 30 minutes, up to 2 hours, to remove surface starch.

Par-cook (blanch) the fries

Drain the soaked potatoes and rinse them under cold water. Pat them completely dry with kitchen towels. Heat vegetable oil in a heavy pot or deep fryer to 325°F (160°C). Working in batches, fry the potatoes for 4–6 minutes until tender but not browned. Remove with a slotted spoon and drain on a wire rack or paper towels. Let cool for at least 15 minutes (can be refrigerated for up to 2 hours).

Finish frying

Heat the oil to 375–390°F (190–200°C). Fry the cooled par-cooked fries in batches for 2–4 minutes until golden and crisp. Transfer to a wire rack or paper towels. Immediately season with 2 tsp salt (adjust to taste) and sprinkle 1 tsp black pepper. Toss with 1 tbs neutral oil if you want an extra sheen and even seasoning.

Keep fries warm in a low oven (200°F/95°C) on a tray in a single layer while finishing remaining batches and while finishing the sauce.

Sauce Béarnaise

Clarify butter (optional but recommended)

Melt the 150 g unsalted butter in a small saucepan over low heat until it separates into butterfat and milk solids. Skim off and discard the foam, or pour the clear butterfat into a small bowl leaving the solids behind. Keep warm but not hot.

Make the reduction

In a small saucepan combine 3 tbs white wine vinegar, 2 tbs dry white wine, the finely minced shallot, and 1 tbs of the chopped tarragon. Bring to a simmer and reduce until about 2 tablespoons of liquid remain (about 6–8 minutes). Strain the reduction into a heatproof bowl to remove solids and set aside to cool slightly.

Create the emulsion (bain-marie or whisk method)

Place the strained reduction in a heatproof bowl over a barely simmering pot of water (double boiler) — the bowl should not touch the water. Add 3 egg yolks and 1 tsp cold water to the reduction and whisk constantly until the mixture thickens and becomes pale and creamy (about 3–5 minutes). Remove the bowl from the heat if it starts to get too hot to avoid scrambling eggs.

Incorporate butter

Very slowly, start adding the warm clarified butter in a thin, steady stream while whisking continuously to create a smooth, glossy emulsion. If using whole melted butter, pour slowly and avoid the milky solids. Continue until all butter is incorporated and the sauce is thickened to a creamy consistency.

Finish seasoning

Stir in the remaining 1 tbs chopped tarragon and the optional chervil/parsley. Season with 1/2 tsp salt, 1/4 tsp white or black pepper, and 1 tsp lemon juice (add more lemon to taste). Keep the sauce warm (not hot) by resting the bowl in warm water or in a very low oven (warm setting). If the sauce becomes too thick, whisk in a few drops of warm water to loosen it.