Preheat a large cast-iron skillet over medium-high heat for 1 minute, then melt 1 tablespoon oil. Arrange cabbage cut side down in skillet and cook, turning occasionally, until deeply golden brown, 3 to 4 minutes per side. Transfer cabbage to a plate.
In same skillet over medium heat, heat remaining 1 tablespoon oil. Add chile, garlic, ginger, tomato paste, and turmeric and cook, stirring often, until fragrant, about 1 minute; season with salt. Add chickpeas, milk, bell pepper, and ½ cup water. Nestle cabbage into pan and bring to a simmer. Cover and cook until cabbage is very tender, 20 to 25 minutes.
Stir in lime zest and juice. Top with cilantro.
