Preheat oven to 325°F (160°C).

Let pork sit at room temperature for 30 minutes.

Pat pork dry with paper towels.

Season pork generously with salt and pepper.

Heat vegetable or olive oil in a large Dutch oven over medium-high heat.

Brown pork on all sides (10-12 minutes total).

Remove pork and set aside.

Reduce heat to medium and add 3 tablespoons of butter to the pot.

Add caraway, fennel, and mustard seeds; stir for 1 minute.

Add onions, apples, thyme, nutmeg, salt, and pepper.

Cook until onions begin to soften (5 minutes).

Deglaze the pot with cider vinegar, scraping up any browned bits.

Stir in honey and beer, scraping the bottom of the pot.

Add chicken stock and return the pork to the pot.

Bring to a simmer, then cover and place in the oven for 2.5-3 hours, turning pork halfway through.

Remove pork from the pot; place on a plate and tent with foil to keep warm.

Shred pork with two forks.

Return shredded pork to the braising liquid.

Prepare mashed potatoes and parsnips while pork braises.

Place potatoes and parsnips in a pot, cover with water, and bring to a boil.

Salt the water and cook until tender.

Drain potatoes and parsnips and return to the hot pot.

Mash with milk and remaining 3 tablespoons of butter.

Season with salt and pepper, then add cheddar cheese and mustard.

Taste and adjust seasonings.

Reheat pork, covered, over medium heat, stirring occasionally.

Reheat mashed potatoes and parsnips over medium heat, adding a little stock or milk to loosen.

Serve pork alongside or on top of mashed potatoes, garnished with chopped parsley.