Prepare the monkfish: Season the wild monkfish tail with salt and white pepper on both sides.
Cook the monkfish: Heat olive oil in a pan over medium-high heat. Sear the monkfish for about 3-4 minutes per side until golden and cooked through. Remove the fish from the pan and let it rest.
Cook the asparagus: In the same pan, sauté the asparagus for 3-5 minutes until tender but still crisp. Remove from the pan and set aside.
Make the beurre blanc sauce: In a small saucepan, simmer the shallots with red wine vinegar over medium heat until reduced to about 2 tablespoons.
Add the butter: Lower the heat and gradually whisk in the cold butter cubes until the sauce is smooth and creamy. Strain the sauce if desired.
Assemble the dish: Plate the monkfish and asparagus, then drizzle with beurre blanc sauce. Garnish with fresh parsley.
Serve immediately: Enjoy your delicious, gourmet meal!