Create an Italian herb baste by mixing together the olive oil, Italian seasoning, parsley, basil, shallots, garlic, and Parmesan in a bowl.
Preheat a grill to medium, using mesquite wood. Coat the halibut in the Italian herb baste and place fish on the grill. Grill, turning often to avoid burning, until fish is opaque and a knife slides in easily.
Remove from heat and serve halibut with fresh vegetables and a starch of choice.