Set up your Weber Kettle for indirect grilling – Fill your charcoal chimney fire starter with charcoal briquettes, and when ready, empty the chimney in the center of the charcoal grate. With tongs, move the charcoal to both sides of the Weber Kettle, creating two equal piles.
Make the filet mignon stuffing – Bring the filet mignon to room temperature while you make the stuffing. Place the olive oil in a small sauté pan and add the green pepper, yellow pepper, garlic and crawfish tails and sauté until tender, about 5 minutes. Mix in the bread crumbs and Creole seasoning.
Prepare the filet mignon – With a small sharp knife, cut along the side of the filet mignon to create a deep pocket. Move your knife back and forth in the pocket, widening it as you cut. Stand the filet mignon up with the pocket facing you, and with a small serving spoon, add as much stuffing as the pocket can hold. Push two toothpicks through from side to side. Brush the stuffed filet mignon with olive oil and sprinkle on the Creole seasoning.
Place the stuffed filet mignon on the Weber Kettle grill grate – Place the stuffed filet mignon in the center of the grill grate, equidistant from both piles of the coals. Place the lid on the Weber Kettle and grill for approximately 20 minutes, or until a meat thermometer inserted through to the stuffing reads 135 degrees.
Remove the stuffed filet mignon from the Weber Kettle – Place the grilled filet mignon on a plate and let it rest for five minutes. Serve one stuffed filet mignon for each guest.