Core the cabbage and slice it into 1/4-inch thick ribbons, then dice the onion into 1/2-inch pieces. Mince the garlic cloves fresh (this makes a real difference in flavor), and slice the kielbasa into 1/4-inch thick rounds or half-moons. Having everything prepped and ready before you start cooking ensures the dish comes together quickly and nothing overcooks while you're still chopping.

Heat the olive oil in a large skillet or Dutch oven over medium-high heat until shimmering. Add the sliced kielbasa and cook for 7-10 minutes, stirring occasionally, until the edges are browned and the sausage releases some of its fat. This browning adds depth and develops the sausage's savory flavor. Remove the cooked kielbasa to a plate and set aside.

Reduce the heat to medium and add the butter to the remaining fat in the pan. Once melted, add the diced onion and cook for about 3 minutes, stirring frequently, until the onion becomes soft and translucent. Don't let it brown—we want a gentle, sweet base for the cabbage rather than caramelized edges at this stage.

Add the sliced cabbage to the pan with the softened onions, stirring to coat it evenly with the butter and oil. Cook for 10-15 minutes over medium heat, stirring occasionally, until the cabbage becomes tender and begins to caramelize lightly. I like to give it a gentle stir every couple minutes to ensure even cooking and prevent sticking. The cabbage will wilt down significantly as it releases its moisture.

Add the minced garlic, paprika, and caraway seeds to the cabbage and stir well to distribute the spices evenly. Cook for about 1 minute until fragrant, allowing the garlic to soften slightly. Return the cooked kielbasa from Step 2 to the pan and stir gently to combine everything together, cooking for another 1-2 minutes to warm the sausage through and marry all the flavors.

Drizzle the apple cider vinegar over the dish and give it a final stir—the acidity brightens all the flavors and cuts through the richness of the sausage and butter beautifully. Taste the mixture and season with salt and freshly ground black pepper to your preference. Remember that the kielbasa is already seasoned, so add salt gradually and taste as you go.