Braising is good for tough meats needing long, slow cooking to make them tender. Heart is one of those meats. (Having said that, my mom used to pan-fry sliced beef heart after tossing it in seasoned flour. It was yummy!) I don't know how boar heart would compare- probably it'd be a bit smaller than a beef heart.
For a braise, you'll need to trim off any fatty or gristly parts first. Cut the heart in half, then in slices about 1" thick. Then season the meat with salt and pepper. Toss the meat in some flour, and shake off the excess. Then add it to a heavy pot or dutch oven that has oil heating in it. Brown the meat quickly, then set it aside. Pour off any extra oil. Put some aromatic vegetables (chopped onion and/or leek, chopped carrot and celery, maybe some chopped parsley or other herbs) in the pan and saute them until the carrots start to get a bit brown and the onions/leek turn translucent. Put the meat back in the pot and add some flavorful liquids (broth or stock plus wine). Don't cover the meat in the liquid, or you'd just be boiling it. The liquid shouldn't cover it more than about 1/2 way. Cover the pot tightly simmer on a low heat about an hour. You could also put it in the oven at 350 degrees F for an hour or a bit longer.
This method also works for making braised beef or pork. Fiddle around with the herbs you use and try adding some more veggies: chunk of white or sweet potato, tomatoes, etc.
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