On a side burner or stove top heat the butter, garlic, Worcestershire sauce, hot chilli sauce, lemon juice, and smoked paprika in a saucepan over high heat. Leave the mixture to simmer for 2 to 3 minutes.
Prepare the barbecue for indirect cooking over medium heat (180°C to 230°C). If using a Weber® Q® barbecue, set up your barbecue with a convection tray and a trivet.
Place a teaspoon of the butter mixture over each oyster and top with a sprinkle of the grated Parmesan cheese.
Carefully place the oysters on the barbecue and cook over indirect medium heat, with the lid closed, until the juices start to bubble, 5 to 10 minutes.
Carefully place the oysters on the barbecue and cook over medium heat, with the lid closed, until the juices start to bubble, 5 to 10 minutes.
Remove the oysters from the barbecue and garnish with a sprinkle of the finely chopped chives.
