Heat 15 mL (1 tbsp.) oil in a large saucepan set over high heat. Brown beef cubes on all sides, about 5 minutes. Season with salt and pepper to taste; transfer to a dish and set aside.
Heat remaining oil in the same saucepan set over medium-high heat. Sauté vegetables and mushrooms until they soften and start to brown, 5 to 7 minutes. Season with salt and pepper to taste.
Deglaze with red wine, scraping the bottom to remove browned bits, and cook for 1 minute. Add broth, brown rice and reserved beef cubes. Cover and gently simmer soup until rice and beef are tender, about 40 to 50 minutes. Season with salt and pepper as needed. Serve with crusty bread, if desired.