Place each dough disk onto a lightly floured surface. Use a rolling pin to roll the dough out into a circle with a 10 to 12 inch diameter. Transfer each gently to a cookie sheet dusted with cornmeal or flour. Spread each with 1/2 cup of pesto (about half the recipe). Distribute asparagus evenly over the two pizzas.
Place two pizzas in the oven and bake for 20 to 22 minutes, or until crust is golden and asparagus is lightly browned. Remove pizza from oven. Sprinkle one cup of arugula lightly over each pizza.