In a small bowl, whisk the mayonnaise with the lemon zest and juice. Whisk in the olive oil and season with salt and pepper.
In a large skillet, heat the vegetable oil. Add the shiitake mushrooms and season with salt and pepper. Cover and cook over moderate heat, stirring a few times, until browned, about 8 minutes. Transfer to a plate and let cool to room temperature.
In a bowl, toss the arugula with the shiitakes, mint and dressing. Serve the salad right away.