Prepare the barbecue for direct and indirect cooking over medium heat (190°C to 230°C). If using a Weber Q barbecue, set up your barbecue with a convection tray and a trivet.
Lightly coat the cherry tomatoes with olive oil, then season with salt and pepper. In a food processor blitz together the bread, garlic, parmesan and basil leaves until the mixture has turned into fine crumbs.
Using a basting brush, brush the mushrooms all over with olive oil. Season with salt and pepper.
Grill the cherry tomatoes over direct medium heat (190°C to 230°C) for 4 minutes, with the lid closed, turning once halfway through the cooking time. Cook until the tomatoes have just started to blister. Once cooked, remove from the barbecue.
Assemble the mushrooms by placing the cherry tomatoes into the mushroom cavities. Tear the buffalo mozzarella into small chunks and add to the mushrooms. Top with the blitzed breadcrumb mixture.
Roast the portabello mushrooms over indirect medium heat (190°C to 230°C) for 15 to 20 minutes, with the lid closed. If you are using a Weber Q, place the mushrooms onto the trivet. Roast the mushrooms until the crumbs are golden and the mushroom has cooked to your liking.
Finish the mushrooms with a drizzle of balsamic glaze and garnish with fresh basil leaves.