Prepare the Vegetables: Place the cut cabbage, shredded carrots, sliced garlic, and red chili pepper in a large mixing bowl. Toss to combine the ingredients evenly.
Make the Pickling Brine: In a small saucepan, combine the sunflower oil, water, white vinegar, honey, salt, and black pepper (or ground coriander seeds, if using). Bring the mixture to a gentle simmer over medium heat, stirring occasionally to ensure the honey and salt dissolve completely.
Pour the Brine: Carefully pour the hot brine over the cabbage mixture, ensuring that all the vegetables are covered. Use a spoon to press the cabbage down and mix well, so the brine reaches all the ingredients.
Pack into Jars: Transfer the cabbage mixture and brine into clean, sterilized jars. Pack the vegetables tightly, leaving a little space at the top. If needed, add more brine to cover the vegetables completely.
Cool and Store: Allow the jars to cool to room temperature. Seal with lids and refrigerate for at least 24 hours to let the flavors develop. The pickled cabbage will be ready to enjoy after this time but will improve in flavor over the next few days.
Serve and Enjoy: Use the pickled cabbage as a topping for tacos, sandwiches, or as a tangy side to your favorite dishes.