In a medium bowl, mix together lemon zest, dill, parsley, pepper and salt.
Lightly brush the halibut fillets with one teaspoon each with mustard. Gently press each fillet mustard side down into the herb mixture.
In a large skillet, heat the oil to medium-high and place the halibut portions with the herb crust side down into the hot oil. Sear until you see a golden crust around the edges, about 4 minutes.
Carefully turn the halibut over, and cook for another 4-5 minutes or until the flesh flakes easily with a fork.
Sauce Instructions
Cut the butter into medium (½-inch) cubes and return the butter cubes to the refrigerator to keep them cold, which is very important.
Heat the wine, vinegar and shallots in a saucepan until the liquid boils, then lower the heat a bit and continue simmering until the liquid has reduced down to about 2 tablespoons. This should take about 10 minutes.
Once the wine-vinegar mixture has reduced to 2 tablespoons, reduce the heat to low, take the cubes of butter out of the fridge and start adding the cubes, one or two at a time, to the reduction, while you whisk rapidly with a wire whisk. Finish with capers and pour over sautéed halibut.