Heat the vegetable oil in a large pot over medium-high heat.
Sear the cubed pork shoulder in batches until browned on all sides, about 5-7 minutes per batch.
Remove the pork and set aside, then add the chopped onions, garlic, carrots, and celery to the pot.
Stir in the caraway seeds and thyme, letting them toast for a minute to release their essential oils.
Return the browned pork to the pot along with the stout beer and broth, then stir to combine.
Bring to a boil, then reduce heat to low and cover the pot.
Simmer for about 2 hours, or until the pork is tender and the flavors are well combined, stirring occasionally.
Season with salt and pepper to taste just before serving, and garnish with fresh parsley.