Spray a large casserole or oven-safe saucepan with nonstick cooking spray and set over medium heat. Add the meat (working in batches if necessary) and brown on all sides, turning occasionally, about 4 minutes. Transfer to a plate.
Spray again with nonstick spray and add the onions. Cook, stirring often, until softened, about 4 minutes. Add the mushrooms and continue cooking, stirring frequently, until they release their liquid, about 4 minutes.
Stir in the thyme, caraway seeds, salt and pepper; cook until aromatic, about 15 seconds.
Pour in the broth and beer, stirring until the foam dissipates. Stir the beef back into the stew and bring to a simmer. Cover and place in the oven to bake for 30 minutes.
Stir in the rice. Cover and bake until the meat and rice are tender, stirring once or twice, about 1 more hour.