In an electric mixing bowl, combine 3 cups of the flour, salt, yeast and water. Mix on low speed for 2 minutes. Let dough rest for 5 minutes. With the dough hook, add the olive oil and mix on medium speed for 3-4 minutes or until the dough is sticky, but smooth. Add a little more flour if the dough does not come together. Form the dough into a ball and place in an olive oil coated bowl. Wrap with plastic and place in the refrigerator overnight. The next day, let it sit at room temperature for 2 hours before using.
Preheat oven to 500 degrees or higher if you can. Place Pizza Stones in the oven before turning the oven on if you are using them. Let the stones heat for 1 hour.
On a lightly floured surface form the dough into a circle. Place on a pizza peel that has been dusted with flour or cornmeal.
Sprinkle the dough with the mozzarella cheese and Asiago or Gruyere cheese. Top with the sliced ham and cherry tomatoes. Make a few indentations in the cheese to hold the eggs. Drizzle with olive oil. Bake in the oven for about 8 minutes, or until just about to turn golden. Carefully slide the pizza out and crack eggs onto the top of the pizza. Sprinkle with some parmesan cheese. Place back in the oven and cook another 3-4 minutes or until the eggs cooks. Remove pizza from pans, slice and serve.