Heat 4 tablespoons of olive oil in a pan over medium-high heat. Add the garlic and mushrooms and fry for 3 minutes. Add the pine nuts and peppercorns and fry for 1 minute.
Cut the mozzarella into thin slices and arrange on a large plate. Season with salt and pepper, drizzle with roughly half the squeezed lime juice and the remaining 4 tablespoons of olive oil. Spread the mushrooms evenly on top, then finish with the grated carrots.