Place potatoes into a large pot and cover with salted water. Bring to a boil, then reduce the heat to medium-low, cover, and simmer until just tender, about 15 minutes. Drain and allow to steam dry for 1 to 2 minutes.

Meanwhile, heat oil in a large skillet over medium heat. Cook and stir onion and garlic in hot oil until onion has softened and turned translucent, about 5 minutes. Season with curry powder, garam masala, cumin, salt, ginger, and cayenne pepper; cook and stir for 2 minutes more.

Add cooked potatoes, garbanzo beans, peas, and tomatoes, then pour in coconut milk. Bring to a simmer and continue cooking for 5 to 10 minutes.