Heat 1 tablespoon of olive oil in a large skillet over medium-high heat until shimmering. Add the ground beef and cook, breaking it apart with a spoon or spatula as it cooks, until it's browned and no longer pink, about 5-7 minutes. Season generously with salt and pepper, then transfer the cooked beef to a clean plate, leaving as much flavorful fat in the pan as possible—this fat will help build flavor for the aromatics.
Add the remaining 1.5 tablespoons of olive oil to the pan with the beef fat, then add the diced onion and cook for about 2 minutes, stirring occasionally, until it begins to soften and turn translucent. Add the minced garlic and cook for another 30 seconds until fragrant. Now add the paprika, red pepper flakes, and Italian seasoning, stirring constantly for about 30 seconds—this blooming technique releases the oils in the spices and deepens their flavor significantly.
Add the roughly chopped cabbage to the pan, stirring to combine with the aromatic and spice mixture. Season with salt and pepper, then cook for 7-10 minutes, stirring occasionally, until the cabbage begins to soften and slightly caramelize at the edges. I find that letting the cabbage sit undisturbed for a minute or two before stirring helps develop a bit of color and depth, which adds another layer of flavor to the finished dish.
Return the cooked ground beef from Step 1 to the skillet, then add the tomato sauce, beef broth, balsamic vinegar, Worcestershire sauce, and bay leaf. Stir well to combine everything evenly, then reduce the heat to medium and simmer for 3-4 minutes, allowing the flavors to meld together. The balsamic vinegar and Worcestershire sauce will reduce slightly with the sauce, creating a subtle glaze and adding savory depth.
Taste the skillet and season with additional salt and pepper as needed—I tend to add salt in small pinches and taste between additions since the beef broth and Worcestershire sauce already contribute saltiness. Remove the bay leaf before serving. The dish is ready to serve immediately as a standalone bowl or over rice, mashed potatoes, or egg noodles.