Place beans in a large container with 1 gallon of water and 6 tablespoons of kosher salt. Cover and allow to soak overnight, preferably 24 hours. Drain and rinse the beans well.
In a large saucepan, heat the oil. Add the onions, green pepper, and garlic and sautee until softened.
Add the beans, tomato paste, water, vinegar, sugar, salt and pepper. Bring to a boil, then turn the heat down to a simmer and cover. For "al dente" beans, cook 1 1/2 hours, stirring occasionally. For softer beans, adjust the cooking time longer.