Place the potatoes in a large saucepan with 3 cups cold, salted water. Boil the potatoes until tender, about 8 to 10 minutes. Drain the potatoes in a colander and set aside.
Heat the oil in a large, non-stick skillet. Add the onion, pepper, garlic, tomatoes and cumin and cook over high heat until lightly browned and dry, about 3 to 5 minutes. Stir in the tomato paste, parsley, chickpeas and potatoes and simmer for a few minutes. Season with salt, pepper and cayenne to taste. Let the mixture cool to room temperature.
Coarsely puree the chickpea mixture in a food processor, adding the breadcrumbs as a thickener. (Run the machine in short bursts and don't over-process.) Wet your hands and form the mixture into 4 patties. Arrange the patties on a plate spread with plastic wrap and chill for at least 3 hours.