You should start off by making little aluminum foil trays sized to place each fillet. On the bottom of each tray, grease them with olive oil and put the fillets you will be using to make your Halibut with herbed butter.
Now, take a bowl and mix the chopped tarragon or dill with the melted butter in it along with some salt and pepper for taste.
After you place each of your fillets on trays, spread this mixture over them. Make sure to spread it evenly over the whole fillet including the sides.
You need to broil them for 4 minutes. Then, turn the tray and start broiling them from the other side - for another 4 minutes.
Now that your Halibut with herbed butter is ready, you can serve it with mashed potatoes or a fresh salad, your choice!