To prepare slaw, combine vinegar, sugar, oil, pepper, and salt in a medium bowl, stirring with a whisk until sugar dissolves. Add fennel and onion, tossing to combine. Let stand at room temperature 30 minutes to 1 hour, tossing slaw occasionally.
To prepare burgers, remove sausage from casing. Combine the sausage and the turkey breast. Divide mixture into 4 equal portions, shaping each into a 1/2-inch-thick patty.
Place patties on a grill rack coated with cooking spray; grill 5 minutes on each side. Top each patty with 1 cheese slice; grill 1 to 2 minutes or until burgers are done and cheese melts. Place rolls, cut sides down, on grill rack; grill 1 minute or until toasted. Removing slaw with a slotted spoon, arrange about 1/2 cup slaw on bottom half of each roll; top each serving with 1 patty and top half of roll.