Position a rack in the bottom third of the oven and heat the oven to 325 degrees F. (You want it to be hot and ready, but I tend to delay this until the last couple batches of meat are done so I'm not wasting energy.)
Spread the pork on paper towels to dry for 10 to 20 minutes before browning. (You can use this time to chop the veggies and dice the chipotle peppers). If the meat is very wet, pat it dry first.
In a 6-quart Dutch oven or other heavy-duty pot, cook the bacon in 1 tbsp. of the oil over medium heat, stirring occasionally, until browned but not crisp, (6 to 8 minutes). Using a slotted spoon, transfer to a paper-towel-lined plate and set aside. Do not wipe out the pan!
If your bacon was really lean - you might need to add some oil. You want about 3tbsp worth in the bottom of the pan. You'll want it good and hot. Season about one-fourth of the pork with salt and pepper and arrange it in a single layer in the pot (there should be at least 1/2 inch of space between the pieces). (Personally - I find it takes smaller batches for my dutch oven - but yours might be larger.) Brown well on at least 4 sides, adjusting the heat as necessary; each batch should take about 10 minutes to brown. Transfer the pork to a bowl. Repeat with the rest of the pork, seasoning with salt and pepper before browning. Once all of the pork is browned, remove the pot from the heat to let it cool for a few minutes.
Pour all but 2 Tbs. of the fat from the pot. (If there is not enough, add oil to equal 2 Tbs.) Return the pot to medium heat, then add the onion, celery, and (single) carrot. Season with a pinch of salt and pepper, and cook, stirring often and scraping the bottom of the pot with a wooden spatula, until the vegetables begin to soften, 5 to 6 minutes. Stir in the chipotles, garlic, cumin, and oregano and cook, stirring occasionally, until fragrant, 1 to 2 minutes. Return the bacon to the pot.
Add the beer, stirring with the wooden spatula to dissolve any browned bits on the bottom of the pot. Raise the heat to medium high and boil to reduce by about half, 5 to 8 minutes.
Add the chicken broth and 1-1/2 cups water. Bring to a boil.
Return the pork to the pot along with any accumulated juice. Lower the heat to maintain a simmer.
Crumple a 12x16-inch piece of parchment paper, then flatten it out. (Crumpling makes it easier to manage.) Place the parchment directly on the surface of the stew, allowing the ends to come up the sides of the pot. Cover and put in the oven for 30 minutes.
During this time, chop the carrots, potatoes and shallot. The carrots and potatoes should be in decent sized chunks. The shallots can be added whole if they're small or quartered if large. If you have more time, this is a good time to roast the red peppers. (Unless you just bought them roasted.) Just use an open flame (grill, gas stove, whatever) to char every inch of the surface. When this is done, put the peppers into a bowl and cover it tightly with plastic wrap. The longer it can sit like this and steam the better.
After the 30 minutes are up, add the carrots, potatoes, and shallots to the pot. Cover with the parchment paper and lid, and return it to the oven for another 30 minutes.
Towards the end of this time, take the peppers out of the bowl and with a pair of tongs (if they're still hot) and a knife scrape off the skin. It should come off fairly easily. Then slit the pepper from stem to base and cut around the stem - the stem and the seeds should come out easily. Cut the rest of the way through, and wipe away any seeds and cut out what membrane you can. Then chop.
When that second 30 mins is up, add the peppers. Cover with the parchment paper and lid, return the pot to the oven, and cook until the pork is fork-tender, about an hour more.
Stir in the cilantro. I also like to, degrease the stew by laying a clean paper towel over the surface of the stew and gently pushing it into all the bumps and dips, then quickly peeling it off - repeating as needed till you don't see the sheen of oil on the surface. Season to taste with salt and pepper.
Now -- I find that the stew is always better the next day. So I like to let it cool to room temperature, put it in the fridge, and then warm it up in the oven again the next day (usually ~300 degrees until hot). Or at least - that's the idea. I've not yet done it a day ahead as everyone wants to eat it. I did manage to make it in time for lunch and let it sit at room temp all day and then heat it for dinner though -- definitely worth it.