Season the monkfish fillets generously with salt and pepper on all sides.
Heat the olive oil in an oven-safe pan. Sear the monkfish for 3-4 minutes per side until golden.
Transfer the pan to a 375°F/190°C oven for 8-10 minutes to finish cooking.
Meanwhile, blanch the asparagus in boiling salted water for 3 minutes until tender-crisp. Drain.
For the beurre blanc: In a saucepan, combine the wine, vinegar, and chopped shallots. Reduce over medium heat until you have about 2 tablespoons of liquid.
Add the cream, then reduce heat to low. Whisk in the cold butter piece by piece - each piece should melt before adding the next.
Strain the sauce, then add lemon juice and chopped tarragon.
Plate the monkfish with the asparagus and drizzle with the beurre blanc sauce.
