I have a soapstone stove, so the top of the stove doesn't get hot enough to boil water or fry anything up. But it does do well with slowly cooking soups and stews.
Inside the stove is a different story. I load the stove up with a nice bunch of oak in the morning. When I get home from work there are heavy coals on the bottom of the stove. I borrow one of the grill racks from my gas grill and slip it inside the stove, supported by a few fire brinks to keep it well off the coals.
I will split a whole chicken in half, place it on the grill and close the door of the stove. It not only grills the chicken, it also bakes it at the same time. Tastes better than a bbq joint.
Steaks, burgers, sausage and dogs are all grilled right on the rack just as if you were using the gas grill on the deck. Gives the best tasting meat possible.
Whole potatoes are wrapped in foil and dropped down in the coals. After about 45 minutes, jab one with a fork to see if they are done.
I have also "baked" a hole pork butt and minced it for bbq. But that took a lot of time and coal management. The stove couldn't be too hot or too cold.
Last night I made up a couple of batches of pizza dough. Mixed up the bread flour in a glass mixing bowl, added yeast, salt, sugar and olive oil. Placed the bowl next to the wood stove and let it rise. Tamped it down and let it rise another two times. Tonight I plan to preheat a pizza stone in the stove. Then bake homemade pizza inside my woodstove.
Do I cook with my stove? Every other night I would say!