Preheat the oven to 325°F (160°C).
Using a large casserole or Dutch oven suitable for stove top and oven use, heat 1 tablespoon of the oil on the stove top over medium heat.
Meanwhile, mix together the flour, salt and pepper in a large bowl or on a plate.
Coat the cubed beef in the flour mixture.
Brown the meat in the oil, turning to make sure all sides of the cubes are browned. You may need to do this in batches. Add more oil if necessary. Remove the beef cubes as they are browned and keep warm.
Add a bit more of the oil to the casserole or Dutch oven and sauté the onion until it begins to soften.
Grate in the garlic cloves and add the red peppers and cubed eggplant.
Sauté until the vegetables begin to pick up a bit of colour.
Return the beef to the pan and stir in the beef stock, oregano, passata or tomato sauce and the tomato puree or paste.
Put the lid on the casserole and place it in the oven for an hour.
After an hour, remove the casserole from the oven and stir in the button mushrooms and the zucchini.
Put the lid back on and return the casserole to the oven for an hour to an hour and a half, stirring every half hour.
When the beef is fork tender and the vegetables are cooked through, the stew is done. Divide the stew in half, putting half of it to the side to cool. Refrigerate promptly.