Add the oil to a frying pan and heat over medium. While the pan is heating, core and chop the cabbage.
2 teaspoons oil, ½ medium red cabbage
Cook the cabbage, stirring occasionally, for 15-20 minutes, or until the white parts have turned a lighter purple and it's starting to soften.
Stir in the garlic and cook a couple minutes more.
1-2 cloves garlic
Make a small well in the cabbage and add the mustard and honey to it. Stir as it melts (this makes it easier to incorporate into the cabbage), then add the salt and pepper and mix into the cabbage.
1 teaspoon Dijon mustard, 1 teaspoon honey, ½ teaspoon sea salt, ½ teaspoon black pepper
Add the vinegar and stir to combine. The cabbage will turn a more reddish purple and soften when the vinegar is added. Taste and adjust seasoning as needed. Serve hot.