Place all ingredients in food processor and pulse to combine. Spread along one end of parchment paper and roll into a log. Seal ends and place in refrigerator to harden.
Whisk salt into water to dissolve and add herbs.
Place halibut fillets and brine in non-reactive bowl. Cover with plastic wrap and refrigerate for 20 minutes.
Turn on the grill to heat. Preheat oven to 375°F (190°C).
Remove halibut fillets from brine, rinse and pat dry. Place fillets on lightly oiled grill, skin side up; cook 2 to 3 minutes. Rotate 90 degrees and cook another 1 to 2 minutes. Transfer to glass or stainless steel roasting pan, skin side down. Place a pat of herb butter on the top of each fillet and place in oven. Cook until just opaque in the middle.