Pair rich/meaty/heavy, acidic or slightly bitter foods with tannic wines (wines that give you that bitter, dry-mouth feeling you often get from a red wine). Adding salt will also help balance tannins. For example, charbroiled steak with mustard sauce and Cabernet Sauvignon. If you choose a food that fails to somehow account for the tannins in a wine, it can make the wine taste even more tannic, and sometimes unpalatably bitter.
It may seem strange to recommend adding bitterness to food, because we usually associate bitterness with unpleasantness. But there are many foods that have some bitterness, and that bitterness is enjoyable—a little charring on a grilled steak or a roasted red pepper, for example.
Get a recipe for rich Sharp Cheddar and Bresaola Melt.