To prepare the pizza dough, add water to the bowl of a standing electric mixer. Scatter yeast over the water’s surface. Stir to combine. Let stand until bubbly, about 5 minutes.
Add two cups of the flour, the olive oil, salt, and sugar to the bowl. Using the paddle attachment, mix on low speed to combine, and then increase speed to medium and mix until well combined, about 1 minute. Add remaining flour, about 1/2 cup at a time until the dough clears the sides of the bowl. Switch to the dough hook and knead on medium speed for about five minutes until the dough is smooth and elastic. If the dough feels too sticky, add a bit more of the flour and knead for another minute or two. Transfer dough to a bowl coated with olive oil, turning the dough over once to coat it with oil. Cover with plastic wrap and let the dough rise in a warm place until doubled in volume, about an hour.
Preheat the oven to 475º F. Grease and dust two baking sheets with cornmeal or place a baking stone in the oven (preheat for at least 45 minutes before baking). Gently deflate the dough and turn it out on a lightly floured surface. Divide the dough in half and shape each piece into a ball. Let the dough rest for 10 to 15 minutes as you prepare the toppings.
Working with one at a time, flatten each dough ball on a lightly floured surface, rolling and stretching it into a 12-inch round. Place the dough circles on prepared baking sheets or pizza paddles dusted with cornmeal.
Brush the top of each dough round generously with olive oil. Cover evenly with mozzarella cheese and scatter onion, apricot slices, parsley, and prosciutto over the cheese. Using a vegetable peeler, add strips of Parmesan.
If using a baking stone, slide pizza off the paddle (a baking sheet works just as well if you don't have a paddle) onto the baking stone. If using a baking sheet, place the pan and pizza on the oven's bottom rack. Bake until the crust is browned and the cheese is melted and golden around the pizza's edges, about 12 minutes. Top with arugula and additional Parmesan cheese strips. Drizzle with Sriracha and honey to taste.