Coat cold cooking grate of grill with cooking spray, and place on grill. Preheat grill to 350° (medium heat).
Peel shrimp, and slice in half lengthwise; devein, if desired.
Sauté onion, bell pepper, salt, and pepper in 1 Tbsp. hot oil in a large skillet over medium-high heat 5 minutes or until tender. Transfer onion mixture to a large bowl. Sauté shrimp in remaining 1 Tbsp. hot oil 3 minutes or just until shrimp turn pink. Add shrimp to onion mixture, and toss.
Lightly sprinkle flour and cornmeal on a large surface. Place dough on surface, and roll to a 1/4-inch thickness. Carefully transfer pizza dough to a cutting board or baking sheet lightly sprinkled with flour and cornmeal.
Slide pizza dough from cutting board or baking sheet onto cooking grate; spread 1/3 cup refrigerated pesto evenly over crust, and top with shrimp mixture. Sprinkle with 1/2 cup Parmesan cheese.
Grill, covered with grill lid, at 350° (medium heat) 4 minutes. Rotate pizza one-quarter turn, and grill, covered with grill lid, 5 to 6 more minutes or until pizza crust is cooked. Serve immediately.