For the meatballs: Place the bread and 3 tablespoons water into a medium bowl. Mash to a paste with a spatula. Add the beef, sausage, egg, parsley, salt and pepper. Blend the mixture thoroughly with your hands or a flexible spatula. Form the mixture into 10 to 16 meatballs. Arrange the meatballs on a parchment paper-lined baking sheet until ready to use.
For the hearty meatball stew: Sprinkle the meatballs with the flour and turn to coat with any flour still on the foil. Heat a large heavy nonstick skillet over medium heat for 1 minute. Add 2 tablespoons of the olive oil. Drop the meatballs into the skillet, spaced apart. Cook until the bottoms are set and brown, about 2 minutes. Using a flexible thin spatula, turn each meatball onto an uncooked side and cook until the bottoms are set and brown, about 2 minutes longer. Turn and cook a third side, until set and brown, about another 2 minutes, so the meatballs are browned and set all over. Transfer the meatballs to a large plate.
Heat the remaining 2 tablespoons oil in the same skillet over medium-high heat. Add the onions, peppers, 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Cook until soft, 4 minutes. Add the mushrooms and the remaining salt and pepper. Cook, stirring occasionally, until the mushrooms have softened, about 5 minutes. Add the potatoes, beans, tomatoes, red pepper flakes and broth. Bring the mixture to a boil. Reduce the heat to a simmer, cover the pan and cook until the potatoes are tender and the meatballs are cooked through, about 20 minutes.