Coat cold cooking grate of grill with cooking spray, and place on grill. Preheat grill to 350° (medium heat).
Season flank steak with salt and pepper.
Grill steak, covered with grill lid, at 350° (medium heat) 8 to 10 minutes on each side or to desired degree of doneness. Cover and let stand 10 minutes.
Meanwhile, whisk together oil and vinegar in a small bowl.
Cut steak diagonally across grain into thin strips. Cut strips into bite-size pieces (about 1 cup).
Place pizza crust directly on hot cooking grate. Brush top of crust with oil mixture; layer with pear slices, 1 cup arugula, cheese, and beef strips.
Grill, covered with grill lid, 4 minutes. Rotate pizza one-quarter turn; grill, covered with grill lid, 5 to 6 more minutes or until thoroughly heated. Remove pizza from grill, and sprinkle with remaining 1/2 cup arugula and freshly cracked pepper.
Note: For testing purposes only, we used 1/2 (16-oz.) package Mama Mary's Thin & Crispy Pizza Crusts.
Oven-Baked Pizza With Steak, Pear, and Arugula: Assemble pizza as directed, and bake according to package directions for pizza crust.