Pat the beef dry and season with salt and pepper. Toss the pieces with the flour until lightly coated.
Heat the oil in a large skillet over medium-high heat. Brown the beef in batches, then transfer it to the slow cooker.
Add the onion, carrots, and potatoes to the same skillet. Cook for 3 to 4 minutes, stirring occasionally, then scrape everything into the slow cooker.
Pour the Guinness and beef broth into the slow cooker. Stir in the tomato paste, garlic, and caraway seeds until the tomato paste dissolves.
Nestle the cabbage wedges on top of the other ingredients so they sit partly above the liquid.
Cover and cook on low for 8 hours. The beef should be fork-tender and the cabbage wedges soft but still holding their shape.
Taste and add more salt or pepper if needed before serving.