Season both sides of filet with sea salt and fresh cracked black pepper, set aside
Heat a heavy bottom or cast iron skillet over medium high heat
Add ½ tablespoon olive oil to pan, very shortly after add 2 tablespoons butter (adding butter to hot olive oil raises the smoke point of butter allowing for less buring over higher heat)
Once the butter has stopped bubbling add the filets, cook one side for 6 minutes without turning, while the meat is cooking, braise meat by spooning hot butter over the top of each filet
Add 1 more tablespoons butter to the pan, turn filets over and cook additional 4 minutes for medium cooked steaks
Allow filets to rest 4-5 minutes prior to serving
While steaks are resting, dollop a tablespoon of the cold compound butter onto each filet
Serve with sauteed broccoli rabe