Add the onion to the bottom of the slow cooker. Put the meat chunks on top and sprinkle with the garlic, mushrooms, salt, and pepper. Pour in the broth and cook on high for 4 to 5 hours, until the meat can easily be shredded with a fork.
Remove the meat and mushrooms, and serve over polenta or egg noodles with the sauce on top (below).
For the sauce
Remove 2 cups of liquid from the slow cooker (it's okay if some cooking bits are mixed in).
Melt the butter in a saucepan over medium heat. Whisk in the flour and cook until it darkens in color, but does not burn. Whisk in the cooking liquid and stir until it thickens to the consistency of a gravy.
Mix in the sour cream, mustard, salt, and pepper and serve.