Generously salt all sides of the pork shoulder chunks. Heat oil in a heavy 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 creme fraiche. Simmer until liquid is reduced by half and is slightly thickened, 8 to 10 minutes. Stir in a pinch of cayenne. Transfer pork back to pot; 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.