Preheat a large skillet over medium-high heat. Add the oil and heat for a couple minutes.
Salt the boiling water, add the asparagus and cook for 2 minutes. Drain and reserve on a paper towel-lined plate.
Add the salmon skin-side up to the pan and cook for 4 minutes. Flip and cook skin-side down until the skin is crisped and salmon is cooked just past medium-rare, about 6 more minutes.
Meanwhile, make the hollandaise sauce: Bring a couple inches of water to a simmer in a small saucepan. Whisk together the egg yolks, mustard, cayenne, lemon juice, 1 tablespoon each of the herbs in a medium metal bowl. Set the bowl over the simmering water (do not let the bowl touch the water) and whisk until the hollandaise has thickened, about 2 minutes. You can move the saucepan on and off the heat to regulate the temperature, so the eggs don't cook too quickly.
When the mixture is hot and thickened, gradually add the butter in several batches and whisk after each addition until fully incorporated, about 3 minutes. Add sea salt and white pepper to taste.
Place the salmon fillets and asparagus on individual serving plates and spoon the hollandaise over the top. Garnish with the remaining minced herbs and serve.