Set up the bain-marie: Pour about 1 inch of water into the small saucepan and bring it to a bare simmer — lazy bubbles, not a rolling boil. Set the heatproof bowl over the pan; the bottom of the bowl must sit above the water, never touching it. Put the 3 egg yolks and the 2 tsp tarragon vinegar into the bowl.

Whisk the yolks to a foam: Whisk the yolks and vinegar over the simmering water for 3 to 4 minutes until they turn pale golden, thick and foamy — when you lift the whisk, the ribbon should hold for a second before dissolving. If the eggs start cooking at the edges, lift the bowl off the heat for a few seconds, keep whisking, then set it back down. You are warming the yolks, not cooking them.

Add the butter with the heat OFF: Take the bowl completely off the pan and turn the heat off. Whisking constantly, drizzle in the warm melted butter in a slow, thin stream — drops at first, then a thread. Do not stop whisking, and do not pour the butter in all at once, or the sauce will break. The sauce should thicken to the consistency of mayonnaise. Leave the milky solids settled at the bottom of the melting pan.

Season and thin: Whisk in the 1 tbsp lemon juice, the 1/2 tsp kosher salt and several grinds of black pepper. Taste: it should be bright and buttery with a gentle vinegar hum. If it is too thick, whisk in 1 to 2 tsp warm water. If it needs more zing, add lemon juice a teaspoon at a time.

Hold warm, not hot: Serve right away if you can. If the meal needs a few minutes, cover the bowl with a clean kitchen towel and set it back over the warm (not simmering) water with the heat off — it holds for up to 30 minutes. Never refrigerate it and never reheat it over direct heat; both will split it.