Making the Béarnaise Sauce:

• In a Reduction Saucepan, melt 2 tablespoons of butter over medium heat.   
• Add the finely chopped shallot and sauté for a few minutes until it becomes translucent.
  
• Stir in the fresh tarragon and chervil (or parsley) and continue to cook briefly until fragrant.
  
• 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.
  
• When the reduction is completed let the pan cool to warm temperature (about 100F/ 37C).  Add the water, whisk together the 3 egg yolks.
• 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.
  
• 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.
  
• Once done, remove from heat and season with freshly ground black pepper and a little more salt if needed. Keep warm.

Preheat Oven to 450°F (230°C)

Searing the Steaks:

• Season the filet mignon steaks generously with salt and freshly ground black pepper.
  
• Heat a skillet or ovenproof pan over high heat, then add cooking oil or clarified butter.
• Sear the steaks for about 2-3 minutes on each side, or until they develop a rich crust.
  
• Transfer the pan to the preheated oven and roast for 6-8 minutes for medium-rare (adjust cooking time based on your desired doneness).
• Remove the steaks from the oven and let them rest for about 5-7 minutes.
  

Preparing the Asparagus:

• In a separate non-stick fry pan, melt some butter over medium-high heat.
• Add the asparagus and sauté until they are heated through and slightly tender, about 3-4 minutes. Season with salt and pepper to taste.
  

Plating:

• Arrange the asparagus in the middle of the plate, and place a filet mignon on top of it.
• Drizzle the decadent Béarnaise sauce generously over the filet mignon and garnish with a sprig of fresh tarragon.  
  
• Serve immediately and enjoy your homemade Filet Mignon with Béarnaise Sauce!
• Now you can savor the exquisite flavors of this French classic in the comfort of your own home.
• Bon Appétit!