Heat oil in a pot over medium heat. Cook onion in hot oil until translucent, about 5 minutes. Stir in carrots, garlic, turmeric, salt, and black pepper. Cook and stir until flavors are combined, about 7 minutes. Add cabbage and mix well.
Cover the pot, reduce heat to medium-low, and cook until cabbage is tender but not completely soft, about 20 minutes. Add water if vegetables look dry.