Preheat your oven to 325°F (160°C).
In a large bowl, season the country-style ribs with salt, pepper, and paprika. Dredge the ribs in flour, shaking off any excess.
Heat olive oil in a large ovenproof skillet or Dutch oven over medium-high heat.
Add the seasoned and floured ribs to the skillet and brown them on all sides, about 4-5 minutes per side. Remove the browned ribs from the skillet and set them aside.
In the same skillet, add the sliced onions and minced garlic. Sauté for about 2-3 minutes until the onions become translucent.
If using caraway seeds and allspice seeds, add them to the skillet and sauté for another minute to release their flavor.
Return the browned ribs to the skillet, nestling them among the onions and garlic.
Pour the beef or vegetable broth over the ribs. Make sure the liquid covers the ribs partially but not completely. You want some of the ribs to remain above the liquid.
Cover the skillet with a lid and transfer it to the preheated oven.
Bake the ribs for approximately 2.5-3 hours, or until they become tender. You can check for doneness by gently pulling the meat with a fork; it should easily shred.
Optional: About 15-20 minutes before the ribs are done, add the drained and rinsed sauerkraut to the skillet. This will allow the sauerkraut to heat through.
Once the ribs are tender and the sauerkraut is heated, remove the skillet from the oven.
Garnish the dish with freshly chopped parsley for a burst of freshness and color.
Serve the Polish-Style Country Ribs hot, along with sauerkraut, and consider serving them with traditional Polish side dishes like mashed potatoes or potato salad, or cabbage and onions.