Sprinkle the yeast over 3/4 cup warm (not lukewarm) water in a bowl and leave to sit for a bit.
In a mixer, add the flour and 1/2 teaspoon salt, and with the mixer running on low speed (with the paddle attachment), slowly pour in the olive oil and keep going until it's mixed through. Next, pour in the yeast/water mixture and mix until just combined.
Coat a separate mixing bowl with a light drizzle of olive oil, tip the dough in and form it into a ball. Toss to coat the dough ball in the olive oil, then cover the bowl tightly with plastic wrap and allow the dough to rise for at least 1 hour, or up to 3 or 4 days.
Arrange the oven rack in the lowest position and preheat the oven to 500 degrees F. Drizzle a large baking sheet with olive oil.
Roll out the pizza dough as thinly as possible and place it on the baking sheet. Drizzle over some extra-virgin olive oil, sprinkle over some salt and pepper and place the mozzarella slices all over the dough.
Bake until the crust is golden and the cheese is bubbly, 12 to 15 minutes.
Put the arugula, whole basil leaves and parsley in a bowl and toss with the extra-virgin olive oil and balsamic vinegar. Scatter over the pizza, sprinkle with grated Parmesan and serve.