Wash the cabbage, remove wilted leaves, cut into quarters, and shred into thin strips. Slice the onion, mince the garlic and ginger, and chop the green chili.
In a large skillet, heat the vegetable oil over medium heat. Add mustard seeds and cumin seeds, and listen for them to sizzle. After about 30 seconds, add the sliced onion.
Sauté the onions for 5 minutes until golden brown. Add minced garlic, ginger, and chopped green chili. Cook for another 1-2 minutes until fragrant. Add shredded cabbage, turmeric powder, ground coriander, and salt. Stir well.
Cover the skillet and let the cabbage cook for 10-12 minutes, stirring occasionally. Once tender but slightly crisp, remove the lid and stir in garam masala. Cook for an additional 2-3 minutes.
Remove from heat, squeeze fresh lime juice over the stir-fry, and garnish with chopped cilantro. Serve warm.