1/4 cup dry white wine
1/4 cup white-wine vinegar
1/4 cup finely chopped shallots
2 tbsp. chopped fresh tarragon, divided
3 large egg yolks
1 stick unsalted butter, cut into 8 pieces
1/2 tsp. fresh lemon juice, or to taste
Kosher salt and black pepper
1 lb. asparagus, trimmed
1-2 tbsp. olive oil
4 8-10 oz. beef filet mignons
Minced parsley, for garnish
1. Boil the wine, vinegar, shallots and one tablespoon of tarragon in a small, heavy saucepan until the liquid is reduced to two tablespoons. Then strain it through a fine-mesh sieve set into a medium metal bowl, pressing on and then discarding solids.
2. Whisk the yolks into the vinegar mixture, and then set the bowl over a pan of barely simmering water. Cook, whisking constantly, until the yolks have thickened slightly (do not scramble them). Whisk in the butter, one piece at a time, adding each piece before the previous one has melted completely. (Note: have your butter ready next to you so you don't accidentally overcook the eggs).
3. Remove it from the heat, and whisk in the lemon juice, remaining tablespoon tarragon, about 1/2 teaspoon kosher salt and 1/2 teaspoon pepper (or to taste).
4. Transfer the sauce to a smaller glass bowl, and place it into a saucepan that has boiling hot water in it. Cover it with a lid. This keeps the sauce warm while you grill or roast the filet mignon and roast the asparagus.
5. For the filet mignon, season each steak with kosher salt. If you are roasting the filets in a roasting pan or ovenproof frying pan, heat one tablespoon of the olive oil. When the filets are hot, sear them on all sides until they become golden brown. Transfer the pan to the oven and roast them for seven to eight minutes, turning the filets over after three to four minutes.
6. If you are grilling the filets, grill them over hot coals for about eight minutes per side (five minutes per side for rare).
7. To cook the asparagus, begin by preheating the oven to 400 °.
8. Snap or cut the dry stem ends off each asparagus, and place them on a heavy baking sheet. Drizzle olive oil on them, sprinkle them with salt and pepper and toss them. Roast the asparagus until it is tender, which will take about eight to ten minutes, depending on how thick your asparagus is. Cool it slightly, and serve it warm or at room temperature.