This hearty unstuffed cabbage soup is based on my favorite stuffed cabbage recipe, but is much easier and faster to make. The tangy, slightly sweet, rich broth is one of our family's favorites.
Heat a Dutch oven or stockpot over medium-high heat. Cook and stir beef and sausage in the hot pot until browned, 5 to 7 minutes. Drain excess grease, reserving 2 tablespoons.
Add onion and bell peppers to the same pot with meat drippings. Saute over medium-high heat for 3 to 4 minutes. Add garlic and cook until all vegetables are slightly softened and fragrant, being careful not to burn, about 1 minute more. Pour in beef broth, diced tomatoes, cabbage, and carrots.
Combine tomato sauce, brown sugar, vinegar, tarragon, and Worcestershire in a separate bowl. Stir until sugar is dissolved and add to the pot along with red pepper flakes. Season with salt and pepper.
Bring mixture to a boil; reduce heat and let simmer until cabbage is cooked and flavors have melded, about 45 minutes. Taste and adjust seasonings as needed. Serve.