From The Big Green Egg® Cookbook
For Salsa Verde:
Set the EGG for direct cooking with the Cast Iron Grid.
Preheat the EGG to 450°F.
To make the salsa, place the garlic, basil, parsley, oregano, capers, mustard, and olive oil in the bowl of food processor fitted with the steel blade and pulse for 30 seconds. Season with salt and black pepper and set aside.
Place the tuna in a sealable plastic bag. Pour one-half of the salsa over the tuna, seal the bag, and marinate for 30 minutes. Reserve the remaining ½ cup of salsa. Place the beans, garlic, and cream in a small saucepan on the stove-top and simmer over low heat for 15 minutes. Pour the beans into the bowl of a food processor, add the butter, and pulse until the beans are puréed and smooth. Season with salt and white pepper and set aside.
Remove the tuna from the plastic bag and discard the marinade. Season the tuna with salt and white pepper and place on the Grid. Close the lid of the EGG and cook for 2 minutes per side, for medium-rare. Using a long-handled spatula, transfer the tuna to a rimmed sheet pan.
Place a large spoonful of purée in the center of each plate, place a tuna steak on top, and serve with a drizzle of the reserved salsa. Pass the remaining salsa at the table.