Pick over beans and place in a large container and cover with 4 quarts water. Soak at room temperature for about 8 hours. Drain and rinse.
Place dried chili peppers and shiitake mushrooms in the base of a glass jar and cover with 2 cups boiling water. Let soak for 15 minutes, until peppers have softened. Drain, reserving the liquid and remove the stems.
Place the soaked peppers and mushroom in the base of a blender along with the tomato paste, oregano, soy sauce, jalapeños, cumin, paprika, cayenne pepper, garlic and 1 cup reserved liquid from the peppers. Puree and set aside.
Heat the olive oil in the base of a dutch oven over medium heat. Add the onions and salt and cook stirring often, until onions are browned and reduced, about 10 minutes.
Stir in the chili sauce and cook until fragrant, about 1 minute. Add in the soaked beans and 7 cups of water and bring to a boil. Reduce heat to medium-low, cover and cook for 1 hour.
Stir in bulgur and tomatoes with their juice and cook, covered, until beans are very tender, about 1 hour – 90 minutes.