Season pork chunks generously with salt and pepper; toss to distribute seasonings evenly.

Heat vegetable oil in a large pot over high heat. Brown pork in batches so meat isn't crowded, about 7 minutes per batch. Transfer pork to a plate.

Place onions into the same pot; cook and stir until translucent and the edges brown, 3 or 4 minutes. Add garlic and cook until fragrant, about 1 minute. Stir in apple cider and apple cider vinegar.

Increase the heat to high and stir in mustard and horseradish. Transfer browned pork pieces back to the pot, along with any accumulated juices. Pour in cream and 1/4 cup chicken broth; add more chicken broth to cover if needed. Add sage, thyme, rosemary, and bay leaf; season with a pinch of salt. Bring to a simmer, then cover and simmer over low heat for 30 minutes.

Add carrots, celery, and cayenne pepper; season with more black pepper. Leave uncovered and simmer until meat is tender, about 1 hour. Add peas and simmer for 10 minutes. (Optional: for a thicker sauce, raise heat and simmer until sauce is reduced, 5 to 8 minutes.)

Garnish individual servings with apple strips and chives.