Heat gas or charcoal grill. In 2-quart saucepan, heat beer to boiling. Add bratwurst; reduce heat to low. Cover; simmer 15 minutes.
Drain bratwurst. Place on grill over medium heat. Cover grill; cook 5 to 10 minutes, turning once, until brown.
Spread dressing on cut sides of buns. Place bratwurst in buns; top with cheese, bratwurst and sauerkraut.