Preheat panini press to medium. If using a skillet on the stove, heat over medium heat.
In a small bowl, mix together paprika, oregano, thyme, pepper, garlic powder and salt.
Sprinkle each barramundi filet with a generous amount of blackening spice. Press with back of a spoon to adhere.
When panini press is up to temperature, with butter or coconut oil (I like to use the Kelapo coconut oil spray). If using a skillet, add butter or oil to the pan to coat.
Add filets to panini press (you may need to do this in batches) and close the lid. Cook 4 to 5 minutes, or until fish is opaque and flakes easily with a fork.
If using a skillet, place fish flesh-side down on hot pan. Cook 3 to 4 minutes, then flip over to skin-side down and continue to cook until fish is opaque and flakes easily with a fork.
Serve hot, with a pat of butter or mayonnaise on top.