Bring balsamic vinegar to a boil in a medium saucepan over medium-high heat and reduce it to 1/2 cup, stir in the honey. Let cool.
Toss arugula with vinegar and oil and season with salt and pepper to taste. Lay out 1 slice of beef on a flat surface. Place 1 slice of cheese and two tablespoons of the arugula in the middle of the beef and roll up tightly. Repeat with the remaining beef. Place on platter and drizzle with balsamic reduction.