Place the finely chopped shallots into a saucepan with the wine and vinegar. Reduce this liquid by half on a medium-high heat. Once reduced lower the heat.
Reduce the heat to low-medium. Slowly add in cubes of butter whilst whisking or moving the pan, allowing each block to melt before adding in the next. This will make an emulsion. If you see a splitting effect, remove the pan from the heat and continue adding cold butter and whisking.
Once all the butter is added the sauce be a pale yellow, glossy, and thick consistency. Remove the pan from the heat.
Finely chop the capers, cornichons, and parsley. Fold through the butter sauce.