Preheat the oven to 425°F. Place torn bread on a baking sheet and bake for 5-10 minutes, turning occasionally, until golden brown on all sides. Transfer to a medium bowl and allow to cool. In a medium sauté pan, heat 1 tablespoon olive oil and butter over medium heat. Add the shallot and cook for 2-3 minutes until softened. Season with salt and pepper. Add the garlic and cook another 1-2 minutes. Add the mushrooms and cook for about 5 minutes, until softened. Add the thyme and parsley and stir to combine. Add to bread and toss together. Add remaining olive oil and red wine vinegar and toss to combine. Let stand at room temperature for 5-10 minutes to allow flavors to blend together. Toss with arugula and divide between two plates.