Begin by placing a large skillet over medium-high heat. Add butter and oil, melting them together until the mixture sizzles lightly, about 1-2 minutes.

Once the skillet is hot, add chopped onion. Sauté for about 3 minutes until soft and translucent.

Next, add thinly sliced cabbage into the skillet. Stir well and cook for 4-5 minutes, allowing the cabbage to wilt.

Stir in chopped kale and minced garlic, seasoning with salt and pepper. Cook for an additional 8-10 minutes.

Pour in vegetable stock to deglaze the pan, scraping any bits stuck at the bottom. This should take about 2 minutes.

Let the mixture cook for another minute until well-coated and fragrant. Adjust seasoning if necessary, then serve immediately.