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Ingredients
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Steak
Asparagus
Béarnaise sauce
Method
Steak
Bring to temperature
Remove filets from refrigerator 30–45 minutes before cooking to come to room temperature. Pat dry with paper towels.
Season both sides generously with kosher salt and freshly ground black pepper (about 1 tsp pepper split between the two). Press seasonings lightly to adhere.
Preheat oven to 400°F (200°C). Place a heavy ovenproof skillet (cast iron preferred) over high heat until very hot, about 5 minutes.
Flip filets and add 2 tablespoons unsalted butter, crushed garlic cloves, and thyme sprigs to the pan. Tilt pan and spoon the foaming butter over the steaks (baste) for 1–1½ minutes.
Transfer skillet to the preheated oven and roast to desired doneness: about 4–6 minutes for medium-rare (internal temp 125–130°F / 52–54°C), 6–8 minutes for medium. Use an instant-read thermometer for accuracy.
Remove steaks from oven and transfer to a warm plate. Tent loosely with foil and rest for 5–7 minutes so juices redistribute.
Asparagus
While steaks rest, trim asparagus by snapping or cutting off the woody ends (about the bottom 1–2 inches).
Toss asparagus with 1 tablespoon olive oil, 1/2 tsp kosher salt, 1/4 tsp pepper and the zest of the lemon.
Heat a large nonstick or cast-iron skillet over medium-high heat. Add asparagus in a single layer and sauté, turning occasionally, until bright green and tender-crisp, about 4–6 minutes depending on thickness.
Remove from heat, squeeze half the lemon over asparagus, adjust seasoning to taste, and keep warm.
Béarnaise sauce
In a small saucepan combine tarragon vinegar, white wine, minced shallot, tarragon stems, and 1/4 tsp freshly ground pepper. Bring to a simmer over medium heat and reduce until about 2–3 tablespoons of liquid remain (this concentrates flavor). Strain into a heatproof bowl and discard solids. Allow to cool slightly.
Place the bowl with the reduced vinegar over a saucepan of barely simmering water (double-boiler setup). Add the 3 egg yolks and whisk continuously until the mixture is pale and slightly thickened (the emulsion should reach about 140–150°F / 60–65°C). Be careful to avoid scrambling — keep heat gentle.
Once emulsified, remove from heat and whisk in 1 tsp lemon juice, 1/2 tsp salt, and most of the chopped tarragon leaves (reserve a pinch for garnish). Taste and adjust seasoning.
If sauce is too thick, whisk in a teaspoon or two of warm water to reach desired spoonable consistency. Keep sauce warm (not hot) until plating; hold over warm water or in a thermos for up to 30 minutes.
To serve
Place a filet mignon on each warmed plate. Spoon 2–3 tablespoons of béarnaise sauce over or beside each steak.
Arrange a portion of asparagus alongside the steak. Garnish with remaining tarragon leaves and a light sprinkle of finishing salt or cracked pepper if desired.
Serve immediately.