1. Put the vinegars and finely chopped onion in a small saucepan ; boil steadily until reduced to 1 tablespoon. Strain and set aside to cool.
2. Add the egg yolks and whisk well with a balloon whisk.
3. Place the bowl over a pan of hot water and continue whisking. Gradually add the softened butter, whisking until the sauce thickens and all the butter has been added.
4. Season and serve.