In a large mixing bowl or a mixing bowl of a stand mixer, add warm water, yeast and sugar and give it a stir until the ingredients are combined and dissolved.
Add olive oil, flour and salt to the yeast mixture. If you are using a stand mixer, use the hook attachment and combine the ingredients on low-medium 2 speed until the dough comes together and separates from the bowl. Continue kneading the dough for 4-5 minutes until it becomes smooth and supple. I like to knead by hand for a few minutes to get the smooth texture. The dough will be sticky at first, but it should smooth out, and resist adding anymore then the recipe calls for. Transfer dough to a large lightly greased bowl, turning a few times to coat the dough, then cover with saran wrap and towel. Place in warm area, and allow to rise for about an hour or until the dough doubles in size.
Prepare all the toppings while the dough is rising.
Deflate the dough and place it on clean work surface. Divide the dough in half and shape dough using a rolling pin and your hands, then transfer onto a prepared baking sheet and continue shaping with your hands if needed. Cover with towel, and leave them to rest for 10 minutes if so desired for a thicker crust.
Preheat oven to 475°F and brush 2 tablespoons of olive oil over each crusts. Divide the pesto and evenly spread on each crusts. Do the same for the mozzarella cheese, tomatoes, red onion, artichoke hearts, black olives, oregano, feta and a few sprinkles of sea salt. Bake for another 12-15 minutes.
Drizzle with some olive oil and sprinkle with Parmesan cheese. Garnish with salad greens and parsley. Serve immediately and enjoy!