Gather and prep your ingredients. Get your grill fired up (direct heat).
Lightly season both sides of the halibut with the salt & pepper.
In a pan over medium heat, cook the olive oil and garlic.
Drop heat to low and add the butter. Melt.
Remove the baste from the heat. Add the chopped basil.
Apply some olive oil to the grill grate to prevent sticking and place the halibut on the grill flesh side down for 2 minutes. This will give it some nice grill marks.
Flip the halibut and continue cooking.
As the halibut cooks, baste it with the basil sauce.
Continue to cook until internal temp has reached 135 degrees. Note that this basting fluid is combustible and you'll get some flareups. That's fine. Just don't let the halibut overcook.
When finished, plate the halibut. Drizzle any extra basil baste on the top. Garnish to your pleasing (I used Parmesan and some extra basil here). Enjoy!