Mix steak seasoning, 3 tablespoons olive oil, 3 cloves minced garlic, pepper and BBQ sauce. Divide in half, saving half for grilling. Brush both sides of steaks with remaining mixture. Refrigerate 2-3 hours.
Bring steaks to room temperature before cooking.
To make the sherry mushrooms, heat 3 tablespoons olive oil in a large skillet over medium heat. Add green onions and cook until soft. Add 2 cloves minced garlic and cook 1 minute. Add mushrooms and increase heat to medium-high. Cook 5-7 minutes, stirring often, until mushrooms give off most of their liquid. Add sherry and tarragon, cooking until liquid is absorbed and mushrooms begin to brown and caramelize. Add cream into mushrooms and remove from heat and cover.
To cook the steak, heat grill to medium-high heat. Place steak on grill and sear for 1 minute. Flip and sear the other side 1 minute longer. Now turn off burners on one side the grill for indirect cooking. Move steaks to the "cool" side of the grill (the one without any burners running underneath). For medium-rare steaks, grill for 6 minutes, then turn and brush the other side of steak with remaining garlic/olive oil mixture. Grill another 6 minutes, and then remove from grill.
Let rest a few minutes before serving and cover steaks with warm mushroom mixture.