In a small bowl, stir the warm water, yeast, and sugar together; allow to rest for 5 minutes.
In a large bowl, add the flour, olive oil, and salt. Pour the water and yeast mixture into the flour bowl and knead the dough for 3-4 minutes, then let the mixture rest for 15 minutes.
Knead the rested dough for an additional 3 minutes until smooth and should still feel a little soft. Poke it with your finger – if it slowly bounces back, your dough is ready to rise. If not, keep kneading. Shape dough into a ball.
Lightly grease a large bowl with oil. Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl with a clean damp kitchen towel. Allow the dough to rise at room temperature for at least 1 hour or longer (if making the dough the day before actually using, then rest and rise for 8 to 24 hours in the refrigerator).
When the dough is ready (it should be doubled in size) punch it down to release any air bubbles. Divide the dough in half. On a lightly floured work surface using lightly floured hands or rolling pin, gently flatten the dough and shape into circles.
Preheat oven to 500°F.
Lightly sprinkle pizza pans with cornmeal and place each dough on top of a pan and shape the edges. Using your fingers, push dents into the surface of the dough to prevent bubbling.
Lightly spread the pesto on each crust. Top with cheese and sliced peaches. Bake for 9-10 minutes, or until cheese is melted and bubbly. Remove from oven.
Layer the prosciutto and arugula onto the pizza. Drizzle with honey, and extra-virgin olive oil to taste. Sprinkle with flaky salt and red pepper flakes. Slice and serve immediately. Enjoy!