In a medium bowl, mix together lemon zest, dill, parsley, pepper and salt.
Lightly brush the flesh side of the halibut portions with one teaspoon of Dijon mustard.
Gently press each halibut portion, mustard side down, into the herb mixture.
Heat the vegetable oil to medium-high in a large skillet, and place the halibut portions with the herb crust down into the hot oil. Alternatively, you could use a stove-top grill in the same way.
Sear the halibut for about 4 minutes, until you see a golden crust around the edges.
Carefully turn the halibut over, and cook for another 4-5 minutes or until finished. Halibut is ready to eat when the flesh flakes easily with a fork.