Combine 1 cup flour, 1 package Fleischmann’s® RapidRise® Instant Yeast, sugar and salt in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead on a floured surface, adding additional flour if necessary, until smooth and elastic, about 4 minutes. Let the dough rest for 10 minutes.
While the dough is resting, make the white pizza sauce. Heat a small pot over medium heat. Add the butter and melt. Add the flour to the butter and whisk to combine into a paste.
Add the milk, parsley, and garlic powder to the sauce. Whisk to combine. Add the Parmesan and remove from the heat. Whisk until the cheese is melted. Season to taste with salt and pepper. The sauce will be very thick.
Pat or roll the dough out on a lightly floured surface until it is approximately 12 inches wide.
Transfer the dough to a greased baking sheet. Form a rim by pinching the edge of the dough.
Spread the sauce along the dough, avoiding the crust edges.
Sprinkle the mozzarella cheese across the sauce. Add the ham and green bell pepper across the pizza.
Brush the edge of the crust with a little more oil and sprinkle with Parmesan or garlic powder, if desired.
Bake on lowest oven rack for 5 minutes. Crack the eggs, scattered across the pizza. Use more eggs if desired. Some of the whites may run off the pizza, which is okay. Season the eggs with a little salt and pepper if desired.
Push the pizza back in the oven and cook until the whites are set, approximately 7 minutes more. Remove the pizza from the oven.
Cut into eights and serve immediately.
Notes: If you do not have a thermometer to measure the temperature of the water, the water should be very warm but not too hot. If too hot, it will kill the yeast and the dough will not rise. If you want the yolks cooked through, add them before the pizza goes in the oven the first time. If you want runny whites, add the eggs 8 minutes into cooking instead of 5.