Unlike proscuitto which comes from the pig, bresaola is a beef product.
Preheat oven to 325 degrees. In a small bowl, toss bread pieces with 1 tablespoon oil; season with salt and pepper. Toss to coat; spread out in a single layer on a rimmed baking sheet. Bake, tossing once, until slightly crisp, about 7 minutes. Let cool.
Toss together arugula, cheese, and bresaola in a medium bowl. Drizzle with lemon juice and 2 tablespoons oil. Season with salt and pepper. Toss in croutons, and serve.