Preheat oven to 425°F. Press pizza dough into a 15- x 11-inch rectangle on a lightly greased (with cooking spray) rimmed baking sheet.
Bake on lower rack in preheated oven until lightly browned and crisp, about 12 minutes. Increase oven temperature to broil with oven rack 3 inches from heat.
Pulse 1 cup basil, peas, parsley, oil, lemon juice, garlic, and salt in a food processor until smooth, about 5 times. Spread pesto over crust, and top evenly with mozzarella.
Broil the flatbread until cheese is melted, about 2 minutes. Top evenly with cooked crumbled bacon and 2 tablespoons basil leaves. Slice the flatbread into pieces, and serve immediately.
