Preheat the oven to 425°F. Cook the bacon in a large nonstick skillet over medium heat until the fat is rendered and the bacon is crisp, about 8 minutes. Remove using a slotted spoon to a paper-towel-lined plate. Add the onions to the bacon drippings and cook until very soft, about 10 minutes. Add the sun dried tomatoes, oregano and garlic. Cook until fragrant, about 2 minutes.
Brush the flatbread with some of the sun-dried tomato oil, and then spread the onion mixture on the flatbread. Sprinkle with the bacon and provolone and spoon the ricotta in large dollops over the surface. Place the pizza in the oven and bake until the edges of the flatbread are crisp and the cheese is melted and lightly browned, about 10 minutes.
Meanwhile, wipe out the skillet used to cook the onions. Heat the skillet over medium heat and add the oil. Carefully break the eggs into the skillet, sprinkle with salt and pepper and cook until the whites are set, 4 to 5 minutes.
If using lavash, cut the pizza into 4 pieces. Place a fried egg on each piece. Scatter the torn basil leaves over the top and serve immediately.