Preheat a grill to medium. Lightly brush the lavash with olive oil, then grill until marked on the bottom, about 2 minutes. Flip the bread and immediately top with the fontina. Continue grilling until the cheese melts, about 2 minutes. Transfer to a platter and top with the prosciutto.
Combine the arugula, fennel, parsley and red onion in a large bowl. Drizzle with the vinegar and 1 tablespoon olive oil; season with salt and pepper and toss. Pile on top of the pizzas; sprinkle with the gorgonzola.