Toss cabbage and salt in a bowl. Let wilt for 1 hour. Squeeze excess liquid from cabbage; set aside.
Heat oil in a 12" skillet over medium-high heat. Add mustard seeds, asafetida, cumin, and curry leaves; cook, stirring, until fragrant, about 2 minutes.
Add reserved cabbage, turmeric, tomatoes, peppers, and serrano; cook, stirring, until cabbage is crisp-tender, 6–7 minutes. Stir in cilantro, lime juice, and sugar. Season with salt; cook until flavors meld, 3–5 minutes.