Season the beef stew meat with salt and black pepper. Heat about 2 tablespoons oil in a large pot or Dutch oven over medium-high heat.
Sear the beef on one or two sides until browned, then remove it from the pot.
Add the onion, carrots, and garlic. Season lightly with salt and pepper. If the pot looks dry, add up to another 2 tablespoons oil. Cook until the vegetables begin to soften and brown.
Sprinkle in the flour and stir for about 30 seconds.
Pour in 2 cups beef broth, scraping the bottom of the pot to loosen the browned bits.
Return the beef to the pot and add the remaining 2 cups beef broth.
Bring to a simmer, cover, and cook for 30 minutes.
Check the beef. If it is still quite tough, cover and simmer another 15 minutes. Once tender or nearly tender, add the potatoes.
Cover and simmer for about 15 minutes, or until the potatoes are nearly tender and the beef is fork-tender.
Add the cabbage, cover, and cook for 10 minutes.
Stir the cabbage. If needed, cook another 5 minutes uncovered until tender but still with some texture.
Turn off the heat and let the stew cool for about 15 minutes. Taste and adjust the salt and black pepper before serving.