The classic way to do this would be to coarsly shred the meat, spread it out on a rimmed baking tray and broil it, pouring the fluids over it in small amounts and letting the fluids sizzle off and evaporate while the meat crisps. This is a rather big mess, I typically do this step in a giant, oversized cast iron skillet (that I was lucky to find at an auction years ago) on the stovetop, which can be turned down to very low once the meat is heated and crisped and you just pull from the hot pan while building tacos.
Classic carnitas are both crispy and juicy, the juicy is from the braising, the crispy is from the broiling.
I cook my carnitas in the oven in heavy enameled cast iron for 8 hours at 225 or 10 hours at 200, same as I do my pulled pork recipe, which I got from a local chef. I typically put it together right before bed and let it cook while I’m sleeping. This is probably close to what a crock pot does, I just never got comfortable with a crock pot and prefer to use my Le Creuset in the oven.
I use the Cafe Delites carnitas recipe from the internet, but cut back the oregano and cumin to about 1/4 of what they specify, I don’t know if it’s a typo or what, but that recipe has WAY too much cumin and oregano. Last time I had to buy the mexican oregano I use they didn’t have dried leaves, only ground and find I like that even better than the dried leaves, I use a little less when I’m using ground. I spent last spring and summer dialing in my carnitas, cooking them every couple of weeks. My friends, coworkers and dogs all enjoyed that process!
I also brown the meat before the slow cooking. I cut it into largish 3-6” chunks and brown on all sides, carefully watching the “fond” (brown buildup in the pan) to be sure I keep it golden to medium brown and don’t let it burn. When I add the braising fluid the “fond” dissolves and adds rich flavor to the braising fluid. If you are browning in a different pot than you are slow cooking in, be sure to deglaze it with some of your braising fluid and then pour that off into your braising pot. Browning the meat makes the final broiling/crisping of the meat less critical because it already has a good caramelized flavor.
In the morning the house smells wonderful and I pull the pot out of the oven and let it cool enough to handle. I remove the meat from the pan and pull out any chunks of fat and discard them. I cover the meat and put it in the fridge. A whole lot of fluid will have cooked out of the meat, once the fluid has cooled enough I put the whole pot into the fridge and let the fat congeal, I skim that off, usually saving some for frying the carnitas later (or even roasting potatoes in it for a different meal).
Now you’ve got your meat chunks and your fluid and are ready to broil or pan fry to reheat. Because I’ve already caramelized the meat, I can skip the broiling step and still have great flavor, but I won’t get the crispy edges. If things are crazy and / or you don’t have time for the broiling step, coarsely shred the meat and just reheat in the microwave. At a party no one will likely notice that you skipped that step, especially if the meat already has really good flavor.
I have a small household so I will put double servings of the meat with plenty of braising fluid into quart ziplocks and freeze them. I have found that putting the frozen meat with fluid into a heavy covered pan for 15-20 minutes thaws and heats it, then I pull off the cover and let the juices evaporate and have easy peasy weeknight carnitas.
Pork cooks down A LOT, so your final product of cooked meat will probably be about half the size of the piece you started with. A lot of fluid and fat will cook out of the meat. I have learned to start with a piece of pork about twice the size of what I think I need and if I’m lucky enough to have leftovers I freeze as described above.
I have also found I very much prefer pork shoulder to pork butt. It’s a little less fatty and I can taste a subtle difference, although a lot of folks will tell you they are interchangeable. To me, pork butt has an ever so slightly “musty” flavor. I thought for a long time that pork butt came from the back end of the pig but recently looked it up, it is from the pigs front but is a different cut than the shoulder. The muscles are smaller in that area and there is more fat.
I also buy the best meat I can afford, this is true for all the meat I cook but I think is especially important in the TASTE of pork. The last time I bought a piece of pork butt it was from a local discount market. I noticed the meat smelled a little “barnyard”, not bad, just smelled a little piggy, I rinsed it really well, patted it dry and cooked as usual...that barnyard smell was in my finished carnitas and I didn’t like it. It was very subtle, but it was there. That batch ended up being dog food. Now I’m even more careful about getting the best pork I can from a local speciality butcher I have become friends with.