Preheat oven to 400 degrees.
Remove steaks from fridge 30 minutes before cooking. Season generously with salt and pepper. In a cast iron skillet, or oven-safe pan, heat canola oil on high.
Carefully add butter, and gently add steaks to pan.
Add thyme sprig to pan and cook 3-4 minutes or until golden brown. Flip steak, and baste with thyme-butter for an additional 3-4 minutes.
Top with shaved Parmigiano Reggiano and transfer pan to top rack of oven. Cook to desired temperature.
During the last 30 seconds of cooking turn the broiler on, watching closely. Broil just until cheese becomes lightly golden brown.
Allow to rest 5 minutes before slicing.