1. In a large saucepot, combine the potatoes, coleslaw, carrots, and chicken stock. Add 4 cups water; the liquid should barely cover the vegetables. Bring to a boil, then cover halfway and reduce the heat to simmer until tender, about 30 minutes.
2. Meanwhile, in a small saucepan, whisk the beer and mustard. Bring to a boil, then reduce the heat to simmer and add the bratwurst. Simmer gently until cooked through, about 20 minutes.
3. Using a slotted spoon, transfer the bratwurst to the vegetable mixture; discard the beer mixture. Divide the stew among dishes and serve with mustard.