For slaw: Place cabbage and carrot in a mixing bowl and toss together.
Place remaining slaw ingredients into another mixing bowl and whisk together until smooth.
Pour mustard mixture over cabbage mixture and toss together until well combined. Cover and refrigerate for 30 minutes to 1 hour.
For brats: Pour beer into a pot and bring to a simmer. Add brats and continue to simmer for about 10 minutes or until brats have just cooked through.
Lightly grease a grill or grill pan and set over medium-high heat. Sear brats for 2 to 3 minutes on each side. Remove from heat and allow sausages to rest for about 5 minutes.
To assemble: Place a brat into each hot dog bun and top with a large handful of slaw. Serve.