To make the shrimp: Heat the oil in a heavy medium skillet over medium heat. Add the pepperoncini and garlic and cook until fragrant, about 2 minutes. Season, to taste, with salt and pepper. Set aside.
Toss the shrimp in a medium bowl with 2 teaspoons of the pepperoncini oil. Sprinkle with salt and pepper. Prepare a charcoal or gas grill for high heat or preheat the grill pan over a high flame. Grill the shrimp until just cooked through, about 2 minutes per side. Toss the shrimp with the remaining pepperoncini oil to coat.
Meanwhile, to make the salad: Whisk the extra-virgin olive oil and lemon juice in a medium bowl to blend. Season the dressing, to taste, with salt and pepper.
Top the arugula with mushrooms in a large bowl. Season the salad, to taste, with salt and pepper. Surround with the warm grilled shrimp and shaved Parmesan. Add dressing and toss before service. Serve immediately. Mound the salad in the center of large plates.