Bring the filet to room temperature, about 30 minutes. Sprinkle the filet with salt and pepper.
Heat a cast iron grill pan on high heat until a drop of water sizzles on it.
Place the filet in the pan and cook for 3 to 4 minutes, then turn. Put half of the butter on the top of the filet and cook for another 3 to 4 minutes.
Remove from the grill and place on a warm plate. Put the rest of the butter on the filet and cover. Allow the filet to rest for about 5 minutes.
While the steak is resting, put the baby arugula in a bowl and toss with the oil, vinegar, salt and pepper. Divide the arugula into two bowls.
Slice the filet against the grain into very thin slices with a sharp knife. Lay half on each plate on top of the salad, then sprinkle with the macadamias.