Combine the first 6 ingredients in a small bowl. Cover and refrigerate aioli until needed.
Preheat the oven to 400 degrees F. Cut the halibut, widthwise, into 18 strips (about 1/2" thick). Line a baking sheet with parchment paper. Lightly brush one sheet of the phyllo with butter. Top it with another sheet and lightly brush it with butter. Cut the pastry, widthwise, into 6 equal strips. Set a piece of the fish at the end of each strip. Roll the pastry around the fish and set on the baking sheet, seam-side down. Repeat with remaining pastry and fish. Cover the prepared fish with plastic wrap until the next batch is rolled. Lightly brush the tops of the pastry with butter.
Bake for 15 minutes, or until the fish is cooked and the pastry is golden. Arrange the fish on a platter with a bowl of the aioli alongside.
Note: The halibut fillets used in this recipe were about 3 inches wide. Our seafood representatives are happy to remove the skin for you. Phyllo pastry is available in the frozen foods aisle. Thaw before using.