Pat the grouper filets very dry with paper towel. Drizzle with 1 teaspoon olive oil and massage to coat. Lightly season both sides of each filet with salt and pepper.
Preheat a stainless-steel or non-stick frying pan over medium heat. Add 1 tablespoon of olive oil and the butter or ghee. Heat until the butter has melted. Carefully add the fish to the pan and cook, undisturbed until golden brown, 3 to 4 minutes. Flip and cook the other side of the filets until golden brown and the thickest part of the fish is opaque and flaky, around 3 more minutes. Transfer the fish to a serving platter and tent with foil to keep warm.
Wipe the pan clean and add 1 tablespoon olive oil. Add the tomatoes and cook, stirring occasionally, until the tomatoes have lightly blistered, around 2 minutes. Add the shallots and garlic and cook, stirring, 30 seconds. Add the seafood broth, lemon juice, capers and oregano and cook, stirring, until the liquid has reduced by ¼ in volume, around 3 minutes. Taste for seasoning and adjust with salt and pepper as desired. Add the parsley and stir through to combine.
Pour the tomatoes overtop of the fish, drizzle over a small amount of olive oil, and serve with sautéed vegetables, potatoes or rice.