Cook the 5 bean varieties separately in five pots of unsalted water for about 30 minutes: black-eyed beans, piattellini, black beans, borlotti and zolfini. These black-eyed beans are separate from the 1 kg / 2.2 lb used later for the blended base.
Wash the savoy cabbage and carrots, and peel the onions and carrots. Quarter the cabbage and slice it into small pieces. Dice the onions and carrots into similar-sized pieces so they cook evenly.
Pour a generous amount of extra virgin olive oil into a large pot and add the vegetables. Cook over low heat, stirring regularly, until softened.
Add the 1 kg of dried, uncooked black-eyed beans to the softened vegetables, followed by the tomato passata and 5 liters of water. Stir to combine.
Cook for about 1 hour. Stir regularly with a spatula, scraping along the sides to prevent sticking.
Transfer 4-6 laddles of cooked mixture to a food processor and blend until smooth and thick. Pour the blended base into a medium-sized pot.
Add one spoonful of each of the five cooked bean varieties to the blended base, including the separately cooked black-eyed beans. Stir gently to combine.
Cook the ditali rigati in a separate pot of boiling water for approximately 6–7 minutes, checking the package instructions and tasting if al dente.
Drain and add the pasta to the pot containing the bean and vegetable mixture. Stir until evenly combined.