Make the Tarragon Reduction: In the small saucepan, combine the dry vermouth, white wine vinegar, minced shallot, bay leaf, and half of the chopped tarragon (1 ½ tbsp). Bring to a boil over medium-high heat. Cook until the liquid reduces to about 2 tablespoons. Strain through the fine-mesh sieve into a small bowl, discarding solids. Let the reduction cool completely.
Sauté the Mushrooms: Heat 1 tablespoon of avocado oil in the cast-iron pan over medium-high heat. Add the sliced portobellos and cook for 5-7 minutes, stirring occasionally, until deeply browned and caramelized. Transfer the cooked mushrooms to a bowl.
Sear the Sirloin: Add another tablespoon of avocado oil to the pan. Season the sirloin cubes generously with salt and pepper. Place the steak in the hot pan in a single layer. Sear for 3-5 minutes, turning the pieces to create a rich brown crust. For medium-rare, cook to an internal temperature of 130°F (54°C). Remove the steak and add it to the bowl with the mushrooms.
Cook the Asparagus: Reduce heat to medium. Add the final tablespoon of oil. Add the asparagus and sliced garlic, sautéing for 3-4 minutes until bright green and tender-crisp. Transfer to the bowl with the steak and mushrooms.
Create the Pan Sauce: Return the pan to medium-high heat. Pour in the sherry to deglaze, scraping up any browned bits from the bottom. Let it bubble for 45 seconds. Stir in the beef broth and cook until reduced by about half. Remove from heat and stir in the red wine vinegar.
Start the Béarnaise: In the clean, cool saucepan, add the egg yolks and whisk for one minute until frothy. Whisk in the cooled tarragon reduction. Set the pan over very low heat and add 2 teaspoons of the cold butter. Whisk constantly and vigorously until the mixture thickens to the consistency of mayonnaise.
Emulsify the Sauce: Immediately remove the pan from the heat. Whisk in the remaining 2 teaspoons of cold butter to stop the cooking. Begin adding the melted butter, one drop at a time, while whisking constantly. Once emulsified, slowly drizzle in the remaining butter in a thin, steady stream, whisking until the sauce is smooth. Stir in the remaining 1 ½ tablespoons of fresh tarragon and the pinch of cayenne. Season with salt.
Combine and Serve: Pour the pan sauce over the steak, mushrooms, and asparagus and toss to coat. Divide the mixture among four plates. Garnish with fresh chives and serve immediately with the warm béarnaise sauce spooned over the top.
