Using a stand mixer fitted with dough hook, mix flour, water, and table salt together on low-speed until no area of dry flour remains, 3-4 min. Turn off mixer and let dough rest for 20 min.

Sprinkle yeast and sugar over dough. Knead on low-speed until fully combined, 1-2 min. Increase mixer speed to high and knead until the dough is glossy and smooth and pulls away from the sides of the bowl, 6-10 min.

Using fingers, coat large bowl with 1 tbsp olive oil. Transfer dough to prepared bowl and pour 1 tbsp oil over the top. Flip dough over once so that it is well coated with oil. Cover bowl tightly with plastic wrap and let dough rise at room temperature until nearly tripled in volume and large bubbles have formed, 2-2 1/2 hrs.

One hour before baking, preheat oven to 450 degrees and place pizza stone on the middle rack.

Turn dough out onto prepared surface along with an oil in the bowl. Separate dough into four balls. Roll or press dough into flattened circles and create a dent in the center of each (this will help keep the egg in place). Let the dough relax for 5-10 minutes. Using dinner fork, poke surface of each ball of dough a few times and sprinkle with kosher salt. Bake in oven until slightly golden, about 5 minutes.

Remove crusts from oven. Add cheese, garlic, and crack an egg in the center of each. Return to oven and bake until crust is golden brown and the egg is cooked sunny-side up (the yolk should still be runny), approximately 10-13 minutes.

Remove from oven and top with arugula, prosciutto, and more cheese, if desired (and really, how could you not want more cheese?).