I won't exactly recommend this, because it's not at all convenient, but I do it once a year, and nothing else comes close. I slow cook a pork shoulder over wood for about 14 hours. It makes enough for several meals, plus a leftover that freeze very well. Here's how:
Buy a pork shoulder, the bigger and fattier the better. The one in my freezer now is 8 pounds. You need the fat to keep the outside of the shoulder from getting done too quickly, leaving the inside undercooked. The night before you plan to do it, pat the shoulder down with salt, pepper, and paprika, and ginger. Also, sometime before you start, find either wood chips, or preferably chunks. Pedagogy varies on what kind--I use a mixture of hickory and mesquite. But be aware--mesquite creates a great taste, but burns hot and keeping the heat down is the key to creating a good barbequed anything.
At around 7am, start the process. I use a large Weber. I put coals in the bottom of the grill and start them. At the same time, put your wood chips or chunks in water. That way they'll smolder rather than burn, and smoke is the basis of a barbecue. When the coals are hot, put the wood on. When you see smoke starting to come up, put the lid on, with a vent partially open.
While this is taking place, make a basting sauce, or "mop." I use three cans of beer, about an equal amount of cider vinegar, paprika, chile powder, and brown sugar. When you've gotten the heat on the grill fairly low, put the pork shoulder one. Remember: THE KEY IS KEEPING THE HEAT LOW. It is the smoke that cooks the pork.
After you put the pork on, mop the other side and turn it, putting the lid back on. You turn and mop about every half hour in the beginning, and then when you're sure the heat isn't too high, about every hour in the end. Yes, it's an all day process, but you don't have to stand over the grill every minute, and it's worth it. You turn, baste, adjust the heat by opening or closing the vent, add coal or wood if necessary, take the lid off if the fire and smoke seem to be dying, and drink lots of beer. In the end, it looks like a work of art. I usually take it off around midnight.
All you have to do is to keep the goal in mind: you are bathing it in smoke, not cooking it by the coals.
When it's off, you can let it cool overnight with a cloth over it. Then you tear off the fat and begin puling the pork apart--that's why it's called "pulled" as opposed to "chopped." If you haven't quite cooked it through (that happens), it's not cheating to stick it in the oven for an hour. And when you do, you'll be able to smell the 12-14 hours of smoke.
From there, you simmer it in a bbq sauce. I could tell you how I make mine, but it doesn't matter much. The flavor comes from the long smoking process. I know it sounds challenging, but oh my, is it worth it