1. Preheat oven to 450 degrees. On a rimmed baking sheet, toss together mushrooms, onion, garlic, and 1 tablespoon oil; season with salt and pepper. Roast until mushrooms begin to brown, about 20 minutes, tossing halfway through. Place prosciutto on another rimmed baking sheet lined with parchment. Bake until prosciutto begins to darken, 8 to 10 minutes. Let vegetables and prosciutto cool on sheets. Break prosciutto into pieces, set aside, and reserve sheet.

2. Cut 1 piece or a 10-inch flour tortilla into 8 wedges; place on baking sheet. Top lavash with cheese. Bake until cheese melts and lavash edges are golden brown, 1 to 2 minutes.

3. Peel roasted garlic and place in a large bowl; mash with a fork. Add 2 tablespoons each oil and fresh lemon juice; season with salt and pepper and whisk to combine. Add roasted vegetables, arugula, and prosciutto crisps. Gently toss to combine. Serve salad with cheese crisps.