Combine olive oil, vinegar, mustard, sugar and salt and pepper in a large ceramic bowl, whisk to combine. Add the mushrooms and stir to coat. Cover and stand 15 minutes.
Preheat barbecue plate on medium-high. Add mushrooms and any remaining dressing and barbecue for 3-4 minutes or until light golden and just tender. Remove to a bowl. Add the asparagus, barbecue 2-3 minutes, turning until tender and just charred. Remove to a plate.
Arrange the salad leaves on a platter, top with avocado, capsicum, asparagus, mushrooms and bocconcini. Season with salt and pepper, drizzle with extra virgin olive oil. Serve with barbecue steak, chicken or lamb.