Epoisses has to be one of the most difficult cheeses to match, not least when it gets to the almost liquid stage shown in this photo (a stage too far IMHO)
It’s one of France’s most notorious ‘stinky’ cheeses - so described because the process of washing the rind in marc de Bourgogne contributes to the cheese’s pungent smell and fluid texture.
The locals like to drink it with red Burgundy (the natural terroir-based match as it's also made in the Côte d’Or) but in my view it almost always slaughters the wine. It’s also - unlike many cheeses - a bit rough on the local dry whites.
The most successful matches I’ve come across are Sauternes, strong Belgian beers and, on my recent trip last week, marc de Bourgogne itself which makes a lot of sense given that it’s used in the cheese’s production. It’s strong but then so is the cheese and it’s woodiness and spiciness deal better with its bitter notes than the intense sweetness of fortified wines like port (though I suspect drier Madeiras and possibly whisky could work too).
If you feel deprived if you don’t have a glass of red wine in your hand while you’re eating cheese try a strong funky red (an old vintage of Chteauneuf-du-Ppe, for example). We tried a slightly less far gone cheese at the Beaune wine bar Le Comptoir des Tontons with Philippe Jambon’s Les OH de Balmont, a vin de table from a natural wine producer in in Beaujolais and they paired remarkably well.