Place the butter in a small bowl and beat until lightened. Mix in the garlic, basil, lemon zest, salt and pepper. Place a foot long sheet of plastic wrap on a work surface; spoon on the butter. Roll the butter inside the plastic wrap into in a 1” thick log. Place in the fridge until firm, about 1 hour.
Preheat your grill to medium-high. Slice the butter into 1/2” thick rounds and set on a plate. Pat the halibut dry with paper towel, brush with olive oil, and season with salt and pepper. Lightly oil the bars of the grill. Grill the halibut 3 to 4 minutes per side, or until just cooked through. Set the fish on plates, top each with 2 to 3 rounds of the butter, and serve.