Beef fillet with shallots cooked in balsamic vinegar and sugar, sauce bernaise

Peel anc clean the shallots, in a casserole, cook them for some second in oil, season with salt and cover with cold water.  Let them cook for about 10 minutes, add balsamic vinegar and sugar, cook untile tender and caramelized, keep warm.
Warm a steel or iron pan, add some butter and cook the fillet to the desired point (44-48°C /111-118°F bleu, 50-55°C / 122-132°F saignant, 58-60°C / 136-140°F à point, 65-68°C / 149-154°F bien cuit). Once the meat is cooked let it res for some minutes away from heat, season with fluer de sal (or kosher salt) and serve it with shallots and a spoon of sauce bernaise