1. Preheat the oven to 200°C (400°F). Heat a teaspoon of oil over medium heat in a saucepan with a lid. Add the red cabbage, cover, and cook for 10 minutes.
2. Reduce the heat, add the garlic, ginger, soy sauce, rice vinegar, and star anise. Add a little water, cover, and cook for 30 minutes, stirring often, until the red cabbage is tender.
3. Meanwhile, arrange the cubes of sweet potato in a single layer on a baking sheet. Brush them with 1 teaspoon of oil, season with salt and pepper. Bake for 35 minutes, flipping them halfway through. Place the Brussels sprouts on a second baking sheet and cook them with the sweet potatoes for 20 minutes.
4. While the vegetables are cooking, cook the rice according to the package instructions, then drain well.
5. Heat a non-stick skillet over medium heat, add the remaining oil and cook the fried eggs for 4 to 5 minutes.
6. Divide the rice, red cabbage, sweet potatoes, and Brussels sprouts into 4 bowls. Place the fried eggs on top, then the green onions, and serve immediately.