Prepare the pizza dough up until the point when you are ready to roll it out and bake (if making Weeknight Whole Wheat Pizza Crust, you can find the directions here.)
Place a rack in the top-most position of your oven and preheat the oven to 500 degrees F (if using a pizza stone, preheat the stone also). If your oven does not heat this high, preheat to the highest possible setting.
Heat a medium skillet over medium low. Once the skillet is hot, add the diced bacon and cook until crisp-tender and the fat has rendered, about 8 minutes. With a slotted spoon, remove the bacon to a paper towel–lined plate and lightly pat dry. Discard all but 2 teaspoons of bacon fat from the skillet, then increase the heat to medium high. Add the mushrooms and cook until tender, about 6 minutes. Remove from the heat and set aside.
On a lightly floured work surface, roll and stretch the dough into a 13-inch circle (if using a pizza stone or round pizza pan) or an 11x14-inch rectangle (if using a baking sheet). If using a pizza stone, for easy transfer, lift the dough onto a sheet of parchment paper set on the back of a baking sheet. (If using a baking sheet, line your pan with parchment paper and place the dough on that). Sprinkle the dough with the mozzarella, half of the Parmesan, and all of the bacon and mushrooms, leaving a 1-inch border around all sides. Make small wells in the center of the toppings for the eggs. One at a time, crack the eggs into a small bowl, then carefully pour into the wells. Sprinkle with the remaining Parmesan. If using a pizza stone, carefully slide the pizza (paper and all) onto the stone.
Bake the pizza on the top rack until the crust is golden, the cheese is melted and bubbly, and the eggs are almost (but not quite) cooked all the way through, about 8 minutes. Remove from the oven and let stand a few minutes. Sprinkle generously with black pepper, then top with fresh parsley. Enjoy immediately.