Adjust oven racks to the top and bottom positions; preheat to 500 degrees F.
Divide the pizza dough in half and roll into two 10-inch rounds. Place the rounds on the backs of two upturned rimmed baking sheets. Brush the edges of the crusts with the olive oil. Divide the mozzarella between the crusts. Sprinkle the bacon evenly over the tops, scatter with the shallots and dot with the tomatoes. Sprinkle with the pepper flakes and Parmesan.
Place one baking sheet on the bottom rack and the other on the top. Bake for 7 minutes. Rotate the baking sheets and continue to bake until golden brown and bubbling, another 7 minutes. Remove from the oven and slide the pizzas onto a cutting board. Top with the avocado slices, scatter with the arugula and season with a pinch of salt. Drizzle with additional olive oil if desired.