There are people who have patience for smoking/roasting a pork butt or shoulder on a Webber grill, adding coals and wood chips for hours, keeping the temp of the grill low, ending with a falling-apart, smoky chunk of pork. I am not one of those people.
Not only do I not have the skills to keep the grill at a low temp (but I am a champ at regular grilling, just saying) but I don't have the patience to hang around the grill, futzing with the coals, the meat, the drip pan, all of it. But who doesn't like a chunk of pork that is lusciously juicy, tender and ready to be rolled into a tortilla?
Enter the overnight roasting plan. (It won't be smoky but it will be amazing!) Whatever cheap cut of pork you get, a shoulder, a butt, bone in or out, it all works. You make a rub (recipes abound online but mine is below) and slather it on the pork. Let it set at room temp for at least an hour, or in the fridge for all day, but pull it out of the fridge at least an hour before roasting. Then find a vessel that it will fit in rather nicely, which means not too huge. It can be an oven-safe saucepan (most of them are) or a casserole or anything that will hold your pork without a ton of room around it. I actually line a smallish casserole with tin foil, then loosely wrap the pork in another layer of foil to make sure it cooks in close proximity to the juice it will throw off. Once you are ready to cook, put the pork in the pot, cover it tightly (more foil it a lid isn't available) and put it in a preheated 350 degree oven. Then, very important, turn the heat down to 220. Go to bed.
That's it. Let it roast for at least 8 hours, more if it's a big chunk. Your kitchen will smell amazing. After the allotted amount of time, turn the oven off and just leave it in there for another hour to cool down. Then take it out, unwrap it, stick a fork in it and Voila! It should be incredibly tender and juicy. If it's not, (because maybe your pork chunk was REALLY BIG) put it back in the oven, turn it to about 300 and cook it another hour. But I doubt this will be necessary.
You can shred it with two forks or tear it apart any way you want. Then you can eat some, drain off the juice and put the juice in the fridge to solidify the grease. The grease can be used to fry some of the pork shards into carnitas, or you can do that in neutral oil as well. The juice, minus the fat, can be used in many ways, just don't toss it. If you have no use for it, freeze it and add it to the next soup or casserole you make. That juice is money, I am telling you!
So, for so little work other than making a dry rub, you get amazing results. I have done this three times, and because I am a single person, I do it with about a pound and a half of a chunk of pork. But it works with double or triple that. Start small, then go big or go home. Just saying.....
The rub: I use a scant quarter cup brown sugar and then any of these spices: cumin, smoked paprika, garlic powder, cayenne powder or chipotle powder or chili powder, lots of salt and pepper, red pepper flakes if it needs more heat. Yesterday I crushed some Sichuan pepper kernels and added those. Taste the rub. It should be slightly sweet and salty and spicy. Adjust. But really, you can't go wrong with whatever you add. I also added some dried oregano but not necessary.
OK, have at it. You will be amazed at the results.