1Preheat the oven to 425 degrees. Toss the mushrooms, onion, half of the tomatoes, 1 tbsp. olive oil, the rosemary, 1/2 tsp. salt and a few grinds of black pepper on a rimmed baking sheet. Roast until the vegetables are tender, about 15 minutes. Slice the mushrooms.
2Meanwhile, combine half of the chickpeas in a medium bowl with 1 tbsp. each olive oil and balsamic vinegar and smash with a fork. Season with salt and pepper. Spread on lavash and top with muenster and parmesan.
3Drain any liquid from the vegetables; arrange lengthwise down the center of the lavash. Top each with 1 cup arugula, then roll up, starting with a long side. Arrange on a baking sheet ; bake until toasted and the cheese melts, about 5 minutes.
4Whisk the remaining 1 1/2 tbsp. olive oil and 1 tbsp. balsamic vinegar in a large bowl. Add the remaining tomatoes, chickpeas and arugula; season with salt and pepper and toss. Slice the wraps into quarters. Serve with the salad.