De-stone the cherries (over a bowl to catch all the juice). Peel the shallots.
Melt the butter in a frying pan and brown the shallots all over.
Add the cherries and their juice, the vinegar, the stock and the wine and cook over a low heat for about 15 minutes until the shallots are cooked through and the liquid has reduced by at least half – you want the sauce to be quite syrupy.
Add the Kirsch and boil for a further couple of minutes.
Taste for sweetness – because my cherries were quite tart, I added 2 heaped tbs granulated sugar but start with 1 tbs if you have sweet cherries.
Boil briefly and then add the lime zest.
Season well with sea salt and black pepper and taste again to make sure you have the right balance between sweet and sour.
Add a touch more sugar if necessary and bring the sauce to the boil to melt the sugar.
This sauce can be reheated easily if you want to serve it hot or simply left to get cold – bring it back to room temperature if you have to put it in the fridge.