To make the dressing, crush and sieve the peppercorns and transfer to a small saucepan. Add teriyaki, mirin, lime juice and ginger .Bring to the boil over medium heat and cook for 1 minute. Set aside.
Thread mushrooms, carrot, daikon and green onions onto skewers. Brush skewers with peanut oil and season with salt and pepper.
Preheat a lightly greased barbecue grill on medium heat. Place skewers on barbecue, brush with dressing and barbecue, turning often, for 5-6 minutes until mushrooms are warm. Transfer to a serving plate and drizzle with remaining dressing and serve.