Cut pork roast into bite-size cubes, trimming off fat as needed. Put pork into a ziploc bag or container with lid. Add 1/4 cup all-purpose flour, 1 tsp salt, and 1 tsp pepper. Shake or stir to mix until the pork pieces are evenly coated. Set aside.
Cut the potatoes and cabbage into bite-sized pieces. Place into a large bowl and set aside. Next, chop the onion into medium-sized pieces (about 1-inch). Slice the celery stalks into pieces and cut the carrots into coins. Mince the garlic.
Preheat oven to 300 degrees F. Place a dutch oven on the stovetop and heat 1 tbsp olive oil in it over medium-high heat (use medium heat if your stove runs hot). When hot, add the pork pieces. Don't overlap them--you may need to work in batches. Cook on each side for about 2 minutes until brown and lightly crispy. They do not need to be cooked all the way through. Remove the pork and set aside.
Add another tablespoon of olive oil to the Dutch oven and add the onion, celery, carrots, and garlic. Cook for 2 minutes, then sprinkle the other 1/4 cup flour and remaining 1 tsp of salt on the veggies. Cook for another 2-3 minutes.
Add the chicken broth slowly and use your spoon or spatula to help deglaze the pan. Scrape any brown bits off the bottom into your broth for flavor. Then add the Guinness and balsamic vinegar, followed by the bay leaves and caraway seeds.
Add the rest of the ingredients in the following order: potatoes, followed by the cabbage, followed by the pork on top. This will keep your pork out of the liquid to help preserve your crispy edges while it stews.
Place the lid on the Dutch Oven and put it in the oven. Cook for about 2 1/2 hours until pork and potatoes are fork tender.
Remove the stew from the oven and remove the lid. Stir to combine the pork and cabbage into the liquid. Your stew is ready to serve.
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Notes
Store leftovers in an airtight container in the refrigerator. This stew is good for 3-4 days after making. It is best reheated in a pot on the stove over medium-low heat.