Season the Halibut fillets with salt and freshly cracked black pepper
Heat a large cast iron, non-stick or fish friendly skillet over medium high heat and add the butter and oil, combining the two as the butter melts.
When the butter/oil is hot but not smoking, add the halibut fillets flesh side down. Let the fillets cook in the pan for about 5 minutes or until the flesh side down has formed a nice golden-brown crust and comes off the pan easily.
Flip the fish to skin side down and finish cooking, turning the heat down to medium if needed. Fish typically cooks 10 minutes for every inch of thickness. This is true for most medium to thick fleshed fish such as halibut, salmon, swordfish, etc.
When the fish is done, transfer to a platter and keep warm.
Let the skillet cool a bit. Then, over medium heat, add the unsalted butter to the fish pan and let it melt. Add the sliced fennel bulb and allow it to caramelize a bit, turning golden brown. Just before the fennel is done, add the garlic and cook for one minute longer.
Stir in the 1/4 cup of white wine and chopped fresh herbs. Let the wine reduce by half and then add the orange zest and green olives.
Hold the skillet over the heat just until the mixture is warmed through, season the mixture with additional salt and pepper to taste, and add one more pat of butter. Let the butter melt and then divide the fennel mixture onto two plates.
Top the fennel mixture with a piece of halibut and garnish with additional chopped Italian parsley and orange zest.