Pat your filets dry with a clean cloth or paper towel, then coat evenly with salt and pepper.
Heat a cast iron skillet over medium-high heat, then add oil.
Place filets in the hot skillet to sear for 2-3 minutes.
Flip the filets, add butter, rosemary, and garlic to the skillet, and cook for 2 -3 minutes, continually basting the steak, garlic, and rosemary in butter.
Remove your filets from heat and allow them to stand for 30 seconds to 1 minute.
Serve atop a bed of sweet potato puree, and enjoy!
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Notes
Ensure your skillet is hot enough that water beads before adding oil and filets. Not only does this give a much better sear with a caramelized crust, but it also prevents your meat from sticking to the skillet.
Don't overcrowd the pan. If you need to cook your filets separately, do so. Forcing them both into a pan that isn't big enough will result in an uneven cook.
A good sear keeps the flavors and juices locked into your filets. Keep a close eye on your meat and look for signs of caramelization on the outside edges to know when it needs to be flipped.
It's essential to keep basting the steak with the butter for several reasons. Moving the butter around continuously keeps it from burning too quickly in your hot skillet as butter burns very quickly. Also, as you baste, the butter becomes infused with the garlic and rosemary flavors, giving you a more flavorful filet mignon.
When you are ready to slice your filet mignon, cut it against the grain for the most tender results.