Bias-slice turkey crosswise in eight 1-inch slices. Flatten slightly with palm of hand, then season with salt and pepper. Brush with half of the honey mustard.
In a 12-inch skillet heat 2 tablespoons of the oil over medium-high heat. Cook turkey in even layer in hot oil for 2 to 3 minutes on each side or until browned. Layer pears on turkey; top each with a half-slice of cheese. Reduce heat to medium-low. Cover and cook for 3 to 4 minutes or until cheese is melted and pears are warm.
Divide arugula among serving dishes; top with turkey slices. For sauce, whisk remaining mustard and oil along with the vinegar into pan juices in skillet; cook for 30 seconds. Drizzle sauce on each serving. Sprinkle with additional pepper.