In a large skillet or Dutch oven, melt the butter with the oil over medium heat.
Add the fennel seed and toast for about 1 minute, stirring constantly, until fragrant.
Add the finely chopped cabbage to the skillet.
Sauté for 5 minutes, tossing frequently with tongs, until the cabbage begins to wilt.
Cover the pan, reduce the heat to medium-low, and cook for 10 more minutes, or until the cabbage is tender to your liking.
Stir occasionally to prevent sticking.
Season with salt and pepper to taste.
Serve immediately.
Don't skip toasting the fennel seeds. This crucial step blooms their aromatic oils, infusing the entire dish with a deeper, more complex flavor.