Barbecue chicken and cheesy pizza — two of the best things in one!
Heat a lightly greased grill or grill pan to medium-high heat. Brush chicken breasts with 1 tablespoon olive oil and season with salt and pepper. Grill for 7 to 8 minutes on each side. Chicken is done when it feels firm to the touch and a meat thermometer inserted in the center reaches 170 degrees F. Remove the chicken from the grill and let rest for 3 to 5 minutes.
When chicken is cool enough to handle, shred into bite-sized pieces. Toss with the barbecue sauce and set aside.
Onto a floured counter, roll the pizza dough into a 12-inch round or rectangle.
Heat a grill or grill pan to medium heat. Lightly brush one side of the pizza dough with half a tablespoon of olive oil. Place the dough oil side down, and grill until the bottom is nicely browned and firm to the touch, about 3 to 5 minutes. Brush the top side of the pizza dough with the remaining olive oil and flip over. Top the pizza with the shredded barbecue chicken, the red onions, and the mozzarella cheese. Close the lid and let cook until cheese has melted and chicken is heated through, another 2 to 3 minutes.
Sprinkle pizza with shredded cheese while it's still on the grill. Remove chicken pizza from the grill onto a cutting board. Sprinkle with chopped green onion and cut into serving-sized pieces.