Set up an immersion circulator in a large pot and preheat the water bath to 10°F below your desired doneness. (Rare = 120°F, Medium-Rare = 130°F, Medium = 140°F, Medium-Well = 150°F, Well Done = 160°F)
And the steaks to a sealable bag with the sprigs rosemary and crushed garlic. Use a vacuum sealer to vacuum seal the bag.
Add the sealed steaks to the water bath and cook for 2 hours. Add a wet kitchen towel on top to keep the bag submerged.
Remove the steaks and pat dry with paper towels. Season liberally with salt and pepper.
Heat a cast iron skillet to medium-high heat and add the butter. Sear steaks for 1-2 minutes per side or until you reach your desired temperature.
Notes
If you don't have a vacuum sealer, you can use a freezer grade zipper bag and zip almost to closed. Submerge the bag in the water and the air will start to come out and zip once everything is released.
Place some wet towels on top of the steaks so they remain submerged.
Liberally salt and pepper the steak as it draws out some of the moisture which is reabsorbed back in.
Let the filet mignon rest for 5 minutes after cooking so it doesn't lose its tasty juices.