1. In the top of a double boiler — or a heatproof bowl set over a saucepan — whisk together the salt, flour, dry mustard, sugar, and cayenne until evenly combined.
2. Add the egg yolks, which have been lightly beaten, then the melted butter. Whisk to incorporate.
3. With the double boiler off the heat, pour in the milk and vinegar very slowly, whisking constantly to prevent curdling (this technique is called tempering — introducing a cold liquid gradually to prevent the eggs from scrambling).
4. Set the double boiler over briskly simmering water, making sure the bowl does not touch the water. Cook, stirring constantly, until the mixture thickens enough to coat the back of a spoon and reaches an internal temperature of 160°F (71°C), approximately 8 to 12 minutes. The dressing will appear glossy and will leave a clear trail when you draw a finger across the spoon.
5. Immediately pour the dressing through a fine-mesh strainer into a clean bowl, pressing any lumps through with a spatula.
6. Set the bowl over an ice bath or refrigerate uncovered until fully cold, approximately 30 minutes, stirring occasionally. The dressing will thicken slightly further as it cools. Store covered in the refrigerator for up to 5 days.
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