Combine 1 tablespoon of shallots, white pepper, salt, and vinegar in a small non-aluminum saucepan. Reduce by three-quarters to approximately 2 tablespoons. Do not under reduce. The final reduction must be as acidic as possible without boiling away altogether. Remove reduction from the heat. While still hot, strain into a clean heavy non-aluminum 4 cup saucepan. Crush the remaining shallots lightly and add them to the reduction. Set the saucepan over very low heat. Then add 4 pats of butter (about 2 tablespoons) and start whisking. As soon as the first 4 pats of butter have almost melted, add 4 more. Continue in this manner until you have melted all but 8 tablespoons (1/4 pound). All the while you must whisk and continue to add fresh pats of cold butter as soon as the previously added butter has melted. Remove from heat and whisk in the remaining butter. Correct seasoning if needed and serve immediately.