Put a baking sheet in the oven and preheat to 250 degrees F. Whisk 4 eggs, the milk, 1/4 cup cheese, the parsley, 1/2 teaspoon salt and a few grinds of pepper in a baking dish; set aside.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add the pancetta and cook, flipping, until crisp, 4 to 5 minutes. Drain on paper towels; reserve the drippings in the skillet.
Heat 1 tablespoon olive oil in another large nonstick skillet over medium heat. Add the bread to the egg mixture and let soak, turning once, about 1 minute. Add 4 of the bread slices to the skillet and sprinkle each with 1 tablespoon cheese. Cook until golden on the bottom, about 2 minutes. Flip, sprinkle each with 1 tablespoon cheese and cook until golden and the cheese on the bottom is crisp, about 2 minutes. Flip again and cook until the cheese melts, about 1 more minute. Transfer to the baking sheet to keep warm and repeat with the remaining bread and cheese.
Heat the skillet with the pancetta drippings over medium heat. Crack the remaining 4 eggs into the skillet and cook until the whites are set, about 3 minutes. Divide the French toast among plates and top with the fried eggs. Toss the arugula in a bowl with the remaining 1 tablespoon olive oil and a pinch each of salt and pepper. Add to the plates. Drizzle with the vinegar and season with pepper.