Chop the chuck roast into cubes and toss in the flour mixture.
Heat a large Dutch oven-style pot with some olive oil over medium-high heat and add some of the beef to sear on all sides for a few minutes. You may have to do this in batches. Transfer the meat to a plate.
Using the same pot, add 2 Tbsp. olive oil and the diced onion. Cook for a few minutes and then add the mushrooms and eggplant. Cook until everything is well colored and starting to get soft.