Using a larger, thicker steak gives a delicious contrast between the crust on the outside and the tender meat inside. Basting the steak with butter deepens the seared crust.
Carefully pat the steak dry with a paper towel. Season liberally on all sides, including the edges, with salt and pepper. Let the steak rest at room temperature for 45 minutes.
Set the EGG for direct cooking without the convEGGtor at 550°F/288°C.
Add a Big Green Egg Cast Iron Skillet to the cooking grid; heat the oil until it shimmers in the skillet. Carefully add the steak and cook, flipping once, until a golden-brown crust starts to develop, about 3 minutes total.
Add the butter, herbs and shallot to the skillet and continue to cook, flipping the steak occasionally and basting any light spots with butter. Continue searing and basting until an instant-read thermometer inserted into thickest part of the tenderloin side registers 120–125°F/49–52°C for medium-rare, 6 to 10 minutes total.
Transfer the steak to a large platter and pour the juices on top. Let rest 5 to 10 minutes. Carve, serve, enjoy!