Blanch the ramp leaves in large pot of boiling salted water. Submerge them for 1 minute and then remove and cool in a bowl with ice water. Squeeze dry with a paper towel. Chop the leaves and set aside. If you don’t have 2 cups of ramps, a mix of fresh basil leaves and ramps is equally delicious.
Using a mortar to make fresh pesto is both an ancient and enjoyable practice, but, of course, if you’d rather use the food processor, there’s no judging here! Start with pulsing the garlic and toasted pine nuts. Add the cheese and ramps. Begin adding the olive oil in a steady stream. Add salt and pepper. The pesto consistency should be a smooth paste. Taste it and add additional salt or pepper if necessary.
Cut the dough in half to make two long flatbread pizzas. Place parchment paper on the sheet pan and drizzle with olive oil. Using your hands, gently stretch the pizza dough into a long flatbread size, about 4 inches by 10-12 inches. Place the dough on the parchment, side by side. Par bake the dough at 450 degrees for 6-7 minutes, until very lightly golden.
While the pizza dough is baking, quickly slice about four 1-inch-thick slices of fresh mozzarella and cube them.
Remove dough from oven. Spread a thin layer of pesto on the pizza. Place the mozzarella cubes on the pizza leaving spaces on each pie for the eggs. Make a small “well” for each egg with the mozzarella. Gently crack an egg into each well. Sprinkle with sea salt and black pepper. Scatter the peas on top of the pizza, avoiding the egg yolk. Brush the crust of the pie with olive oil for golden color and crispness. Bake for an additional 8-10 minutes until the pizza is a rich golden color. Egg whites should be set and the yolks runny.
Remove from oven. Drape the prosciutto slices on the pizza. Sprinkle with sea salt and pepper. Serve immediately.