In a small sauté pan, heat oil over medium heat. Add mushrooms and cook, stirring frequently, until browned, about 6-8 minutes. Season with salt and pepper. Add roasted red peppers and cook until just warmed. Removed from heat.
Lay tortilla on clean work surface. Spread mustard on wrap. Layer roast beef, cheese, arugula, sautéed mushrooms and roasted red peppers over mustard.
Wrap tortilla into burrito shape. Slice in half to serve.