In the bowl of a food processor combine the flour, yeast, and salt and process with 3 or 4 pulses. With the motor running slowly add the water and olive oil. Continue processing until the dough forms a ball, about 1 minute, then process for 1 minute more.
Grease the inside of a large bowl with olive oil and place the dough in the bowl. Cover with plastic wrap and let the dough rise for 1 hour.
Preheat oven to 450 degrees F. Like a large baking sheet with parchment paper and set aside.
Divide the dough in half and roll out each section into 8-inch rounds. Place pizza bases on prepared baking sheet.
Spread ⅓ cup arrabbiata sauce over each pizza base.
In a mixing bowl, toss shrimp with olive oil until well coated. Divide the shrimp in half and arrange on pizza base. Sprinkle ½ cup of mozzarella cheese on each pizza.
Bake pizzas for 20-25 minutes, or until the crust is golden brown and the cheese is bubbling.
Remove from oven and let cool 10 minutes.
While pizzas are cooling, toss arugula with olive oil, lemon juice, salt, and pepper.
Top each pizza with arugula. Sprinkle with red pepper flakes and enjoy!