Set the EGG for direct cooking without the convEGGtor at 425°F/218°C.
Heat butter and garlic in a Big Green Egg cast iron saucepan until melted, about 1 minute.
Remove from heat and stir in parsley, chives, lemon zest and juice, pepper and salt until well combined.
Grill oysters with the shell on the bottom side for about 4-5 minutes until the meat is firm.
Transfer oysters immediately to a platter. Top each oyster with a little of the herb butter and a drizzle with lemon juice. Top with any freshly minced herbs of your choice. Enjoy!