Place potatoes into a large pot and cover with salted water. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until just tender, about 15 minutes. Drain and allow to steam dry for a minute or two.
Meanwhile, heat the vegetable oil in a large skillet over medium heat. Stir in the onion and garlic; cook and stir until the onion has softened and turned translucent, about 5 minutes. Season with cumin, cayenne pepper, curry powder, garam masala, ginger, and salt; cook for 2 minutes more. Add the tomatoes, garbanzo beans, peas, and potatoes. Pour in the coconut milk, and bring to a simmer. Simmer 5 to 10 minutes before serving.