Brown the beef in a skillet over medium-high heat, seasoning with salt and pepper, then transfer it to the slow cooker.
Add the carrots, chopped onion, garlic, Guinness, beef broth, tomato paste, thyme, and bay leaves to the slow cooker. Stir to combine, cover, and cook on low for 8 hours.
While the stew cooks, boil the potatoes in a large pot of salted water until tender. Drain and set aside.
In the same pot, melt 2 tablespoons butter over medium heat. Add the cabbage and cook until softened. Mash the potatoes with the cabbage, remaining 2 tablespoons butter, milk, and green onions. Season with salt and pepper.
Toss the sliced yellow onions in flour. Heat vegetable oil in a skillet and fry the onions in batches until golden and crisp. Drain on paper towels.
Remove the bay leaves from the stew. Spoon the colcannon into bowls, top with the beef stew, and finish with crispy onions.