1/4pound1 stick unsalted butter, melted just before using
To Cook the Steaks
Heat the water according to your sous vide machine’s instructions to 130° F / 54.4° C for medium-rare steaks, or to the desired finished temperature.
Season the filets liberally on all sides with Kosher salt and freshly ground pepper. Place a thyme sprig on each side of the filets, then place it in a vacuum seal bag or ziplock bag.
Vacuum seal the bag if using a vacuum sealer, or if using a ziplock bag; partially seal it removing as much air as possible, then place it in the water to push the rest of the air out before sealing.
Sous vide the filets for 1 hour at 130° F.
Remove from the water and rest for 10 minutes in the bag.
Remove from the bags and dry with paper towels. Season with a little more kosher salt.
Sear the steaks for about 30 to 45 seconds on each side in a very hot skillet with enough canola oil to coat the bottom of the pan. Add a few tablespoons of butter and the thyme sprigs to the skillet and continually baste the steaks while the sear.
Serve immediately with the Béarnaise Sauce.
To make the Béarnaise Sauce
Place the vinegar, wine, chopped shallots, half of the tarragon, 1/8 teaspoon kosher salt and some pepper in a small saucepan. Bring to a boil over medium heat and simmer for about 5 minutes to reduce the liquid to just a few tablespoons. Cool slightly.
Place the cooled liquid with the egg yolks and 1 teaspoon salt in blender or hand blender container and blend for 30 seconds.
Slowly drizzle in the hot butter while the blender is on to create an emulsion. Add the rest of the chopped tarragon and pulse a few times.
With blender on, slowly pour the hot butter through the opening in the lid. Add the remaining 2 tablespoons of tarragon leaves and blend only for a second.
Keep the sauce warm (but not hot) before serving.
If the béarnaise sauce is too thick, you can blend in a little white wine to thin.
The sauce can be made ahead and reheated over a double boiler.