Wash and pat dry the halibut. Season with salt and pepper and hold in refrigerator.
Heat 4 tablespoons olive oil in a sauté pan until oil just begins to ripple. Add onion, peppers, garlic, and herbs. Cook over medium heat until onions are translucent. Deglaze the pan with the wine and scrape the bottom. Add olives, capers and stock and bring to a boil. Drop the heat to a simmer and reduce to one-third of volume. Set aside and keep warm.
Remove the halibut from the refrigerator and heat the remaining 2 tablespoons of oil and two tablespoons of butter over medium to high heat in a large sauté pan. When the oil starts to ripple, carefully add* the halibut. Cook the fish until browned, about 2 to 4 minutes per side until all fish is done. Set on a platter and keep warm. Bring the sauce back to heat for 2 minutes. Remove from flame and incorporate remaining room temperature butter. Adjust salt and pepper if needed.