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.