Season filet and bring to room temperature, at least 30 minutes.
Mix butter, shallot and tarragon in a small bowl. Set aside.
Heat grill. Oil grill. Pat filet dry and place on grill, just off direct flames, and cook for 2 minutes. Once you flip filet over, spread a little compound butter on top. Continue flipping filet until you have cooked it for 2 minutes on all sides, spreading butter on as you go
Let filet rest for 5 to 10 minutes. Slice and serve hot.