Spray a large cassserole or oven-safe saucepan with nonstick spray and set over medium heat. Add the meat (working batches if necessary) and brown on all sides, turning occasionally, about 4 minutes. Transfer to a plate.
Spray again with non-stick 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.