Pat the halibut pieces dry with a paper towel and season them thoroughly with salt and pepper. Then dredge each piece in flour, knocking off the excess before placing on a clean plate.
Heat the olive oil and 2 tablespoons of the butter in a large skillet over medium high. When the foaming of the butter has subsided, place the halibut pieces in the skillet and pan fry without disturbing them until deeply browned underneath, about 5 minutes. Gently turn them over and cook on the other side for 3 to 5 more minutes, or until done. Transfer the halibut to a clean plate.
Reduce the heat to medium and add the garlic to the skillet. Cook, stirring often, for about 2 minutes or until the garlic is golden brown.
Add the wine and lemon juice to the skillet, swirling the pan and scraping up any browned bits stuck to the bottom. Cook for about 3 minutes.
Add the chopped capers and simmer for another few minutes or until the sauce is slightly thickened and reduced. Turn off the heat, whisk in the remaining 2 tablespoons of butter, and season the sauce with salt and pepper.
Drizzle the sauce over the halibut and garnish with chopped parsley. Serve immediately.