Salt all sides of the pork shoulder chunks. Heat vegetable oil in a pot over high heat. Brown pork shoulder pieces until surface is seared and crusty, about 3 or 4 minutes per side.
Transfer browned pork to a plate. Add onions to oil and reduce heat to medium and season with a pinch of salt and pepper. Cook and stir about 2 minutes.
Add torn sage leaves; cook until onions soften and begin to brown, stirring frequently. Pour cider into pot; stir to deglaze bottom. Raise heat to high and bring to a boil. Stir in cider vinegar. Reduce heat to low.
Transfer pork shoulder pieces to cider mixture. Cover; simmer gently on low 1 hour. Remove lid and turn pieces over. Cover; simmer on low until meat is fork tender, 1 to 2 more hours. Transfer pork to a bowl with a slotted spoon.
Raise heat to high and bring sauce to a simmer. Whisk in heavy cream. Simmer until liquid is reduced by half and is slightly thickened, 8-10 minutes. Toss in a pinch of cayenne.
Transfer pork back to pot and reduce heat to low. Baste pork with sauce while it heats through and becomes perfectly tender, and the sauce is as thick as you want it, about 15 more minutes.
In a large cast-iron pot, melt 1 tablespoon of the butter in 1 tablespoon of the oil. Season the pork with salt and pepper.
Season the pork with salt and pepper.
Add one-third of the pork to the casserole and cook over moderately high heat, stirring occasionally, until well browned, about 8 minutes. Transfer the pork to a baking sheet. Repeat in 2 more batches with the remaining butter, oil and pork.
Add the bacon to the pot and cook until desired doneness; then add to the pork.
Add the pork and bacon back to the pot along with the cider, stock and bay leaves; bring to a simmer. Cover and simmer gently until the pork is tender, 2½ hours. Discard the bay leaves.
In a small bowl, whisk the cornstarch with 1/4 cup of water. Add the cornstarch mixture and the cream to the stew and simmer until the liquid is thickened, about 5 minutes.
Stir in the mustard and sage and season with salt and pepper. Enjoy.