1. For crust: Generously grease a large bowl with olive oil and set aside. Combine water,
sugar and yeast in the bowl of a stand mixer fitted with a dough hook attachment. Mix on low speed until combined, about 30 seconds. Let stand until yeast is foamy, about 5 minutes. Add flour and salt. Mix on medium speed until a smooth dough is formed, about 3 to 6 minutes. Transfer dough to the prepared bowl and cover with plastic wrap. Let rest until doubled in size, about 1 hour 30 minutes.
2. Place pizza stone in the oven and preheat to 500°F. On a lightly floured surface, press dough into a 14-inch round circle. Transfer dough round to lightly floured pizza peel.
3. For topping: Sprinkle Parmesan and mozzarella over dough, leaving a 1/2-inch border. Quickly slide pizza onto preheated pizza stone. Bake, rotating pizza halfway through, until crust is golden brown and cheese is melted, about 5 to 8 minutes.
4. Meanwhile, in a large bowl, whisk oil and lemon juice together. Add beans and arugula and toss to coat. Season with salt and pepper to taste. Top pizza with bean mixture and desired amount of shaved Parmesan. Slice and serve with Pinot Grigio.