Why are my sauces splitting?

Question

Recently all my attempts at sauces are splitting and I'm not sure what's going wrong. Tonight I tried a balsamic vinegar reduction / chicken stock / pan juices recipe to go with my lamb chops, but once again the dreaded split occurred. My wife is patient and forgiving, but I feel like I must be missing something fundamental to get this wrong so often.

Two questions.

1. What could I be doing wrong to cause these sauces to split?
2. What can I do to recover when it happens again?

UPDATE: The Pan juices contained a tbsp or two of olive oil, and some of the fresh herb rub I'd coated the lamb chops in (thyme, rosemary, and mint). I did not drain the pan before starting the sauce. It has crossed my mind that perhaps there was too much oil / fats in the pan at that point? For completeness, I should point out that I also sauteed some chopped shallots in the pan juices immediately before adding the vinegar.

Answer

Gerbil gave the basic reasons as to why this might be happening, but as for the 'how to recover' .... you have a few options:

1. Wait for it to finish separating, and take the oil off, then serve without oil.
2. If you still want some fat for mouthfeel, after separating, you can add some butter back into the warm (but not too hot) sauce, and stir 'til melted and combined.
3. If going for a more gravy-like consistency, after separating, put the oil back into the pan, make a roux and follow the basic procedure for a béchamel, but use the juices in place of the milk.
4. After separating, take some of the non-oil part, add an emulsifier (eg, mustard), then slowly whisk back in some fat, add some of the juices, then slowly add the rest of the fat 'til it's the consistency you want.
5. Put it into a blender an mix (although, open the vent hole, then put a towel over the lid, and hold it down with one hand when you turn it on ... blending hot things can be a mess) or use a stick blender.

In the future, I would separate out the juice & fats before reducing. You never know quite how much fat will render out of a piece of meat, and I feel I can reduce the juices faster when there isn't fat in there, but I've never actually timed it. Or, you can go the roux / gravy route if you're in a hurry.

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