Preheat the oven to 300°. Season the pork with 1 tablespoon of salt and Adobo seasoning. In a large skillet or dutch oven, heat the oil until shiny. Add the pork and cook over moderately high heat, turning, until browned on all sides, 2-3 minutes per side. Transfer the pork to a dutch over or plate if you are using a dutch oven on the stove top.
Add the apple, onion, carrot, celery, garlic, teaspoon of salt and thyme to the casserole and cook over moderate heat until beginning to brown, about 6 minutes. Add the tomato paste and cook, stirring, until it deepens in color, about 2 minutes. Add the wine and bring to a boil. Add the chicken stock, vinegar and honey and bring to a simmer. Add liquid smoke to the sauce. Pour over the pork, cover and transfer the dutch oven to the oven. Braise the pork for about 3 hours, turning once halfway through, until very tender.
Transfer the pork to a plate. Strain the sauce into a large bowl, gently pressing on the solids. Pour the sauce back into the pot. Using 2 forks, shred the pork; discard any large pieces of fat. Transfer the shredded pork to the sauce and stir in the cream cheese. Cover and keep warm.
Meanwhile, in a large pot of boiling salted water, cook the pasta until al dente. Drain the pasta and transfer to the casserole with the sauce. Toss the pasta with the sauce and pork.