In a pot of 6 cups of boiling water, add 2 teaspoons of salt and whisk to dissolve.

Add the fresh parsley to the boiling water and blanch for 30 seconds.

Add the fresh tarragon to the pot and give it a quick blanch.

Remove the herbs from the pot using a fine-mesh strainer and shock them under cold running water to stop the cooking and set the green color.

Place the blanched herbs on paper towels and squeeze out as much moisture as possible.

Place the dried herbs in a blender, add the vegetable oil, and blend for 2 minutes until finely chopped and the oil is bright green.

Pour the finished tarragon oil into a bowl and set aside.

Season four 5- to 6-ounce halibut fillets with 1 teaspoon of kosher salt.

Peel and thinly slice one parsnip.

In a large skillet, combine 2 cups of water, the sliced parsnips, thinly sliced shallot, Parmesan rind, lemon peel, lemon juice, peppercorns, vanilla, and salt.

Bring the mixture to a boil over high heat, then cover, reduce the heat, and let it simmer for 20 to 25 minutes to infuse the flavors.

After simmering, bring the poaching liquid back to a boil.

Add the halibut fillets to the skillet, skin-side down.

Add fresh tarragon sprigs and spoon some of the poaching liquid over the fish.

Reduce the heat to low, cover the skillet, and cook for 4 to 7 minutes, until the fish reaches an internal temperature of 110°F.

Remove the skillet from the heat, keep it covered, and let the fish rest for 3 to 7 minutes, allowing the carryover cooking to bring it to a final temperature of about 135°F.

Carefully remove the cooked fish from the skillet and place each fillet in a shallow serving bowl.

Strain the poaching liquid through a fine-mesh strainer into a measuring cup, discarding the solids.

Taste the broth and adjust the seasoning with a splash of lemon juice and a pinch of salt if needed.

Pour the warm broth around the fish in the bowls.

Garnish each piece of fish with whole-grain mustard, fresh tarragon, and a drizzle of the prepared tarragon oil.