Introduce cabbage, potatoes, carrots, turnips, 1 1/2 teaspoons of salt, and 1/2 teaspoon of pepper to the beef mixture.
Increase the heat to medium-high and cook, partially covered, until the vegetables are al dente, about 25 to 30 minutes.
Remove from heat and let it stand, covered, until the vegetables are fork-tender, approximately 10 minutes.