Place a large pan over medium-high heat, and add oil and butter, stir until melted and foamy.
Add diced onion and cook until soft and transparent, stirring for about 3-4 minutes.
Add garlic, cook until fragrant and soft, about 2-3 minutes.
Add cabbage to the pan and toss. Season it with salt, pepper, and smoked paprika.
Let cabbage reduce by half, for about 10 minutes, stirring occasionally.
Add Worcestershire sauce and fresh thyme. Stir.
Slice smoked Polska kielbasa into thin rounds and add it to the pan.
When cabbage has lost much of its volume and started to turn tender and slightly translucent, with browned bits, and Polska kielbasa has browned slightly, the dish is ready to serve.
Remove from heat and garnish with parsley.