Cut 100g of butter into small pieces. Peel and chop the shallots. Add the chopped shallots, white wine, vinegar, bring to boil and let it evaporate slowly.
When there is no more than the quantity of a tablespoon left, gradually incorporate the cold butter over low heat. Whisk until the sauce becomes smooth, and then add salt and pepper.
Melt 15g of butter in a pan, and when it starts foaming, add the scallops. Add remaining butter and cook the scallops about 1 minute on each side (depending on their thickness). Add salt and pepper. Serve the scallops together with the white butter sauce.