Step 1

In a Reduction Saucepan, melt 2 tablespoons of butter over medium heat.

Step 2

Add the finely chopped shallot and sauté for a few minutes until it becomes translucent.

Step 3

Stir in the fresh tarragon and chervil (or parsley) and continue to cook briefly until fragrant.

Step 4

Pour in the white wine balsamic vinegar and white wine.  Add a pinch of salt.  Allow the mixture to reduce until it's reduced to approximately 1 to 1 ½ tablespoon. This will take some time; be patient.

Step 5

When the reduction is completed let the pan cool to warm temperature (about 100F/ 37C).  Add the water, whisk together the 3 egg yolks.

Step 6

A very low burner, continue whisking while maintaining the temperature around 100-110°F (38-43°C). Do not let it get too hot to avoid scrambled eggs. Using a whisk, keep mixing for as long as it takes for you to be able to see the bottom of your pot when the eggs are starting to cook and congeal.

Step 7

Slowly incorporate the clarified butter into the egg yolk mixture, whisking continuously. Add a small amount at a time and ensure it's fully incorporated before adding more.  Continue adding the clarified butter until you achieve a silky, mayonnaise-like consistency.

Step 8

Once done, remove from heat and season with freshly ground black pepper and a little more salt if needed. Keep warm.

Step 9

Season the filet mignon steaks generously with salt and freshly ground black pepper.

Step 10

Heat a skillet or ovenproof pan over high heat, then add cooking oil or clarified butter.

Step 11

Sear the steaks for about 2-3 minutes on each side, or until they develop a rich crust.

Step 12

Transfer the pan to the preheated oven and roast for 6-8 minutes for medium-rare (adjust cooking time based on your desired doneness).

Step 13

Remove the steaks from the oven and let them rest for about 5-7 minutes.

Step 14

In a separate non-stick fry pan, melt some butter over medium-high heat.

Step 15

Add the asparagus and sauté until they are heated through and slightly tender, about 3-4 minutes. Season with salt and pepper to taste.

Step 16

Arrange the asparagus in the middle of the plate, and place a filet mignon on top of it.

Step 17

Drizzle the decadent Béarnaise sauce generously over the filet mignon and garnish with a sprig of fresh tarragon.

Step 18

Serve immediately and enjoy your homemade Filet Mignon with Béarnaise Sauce!

Step 19

Now you can savor the exquisite flavors of this French classic in the comfort of your own home.

Step 20

Bon Appétit!