Heat a large skillet on medium heat. Place the olive oil and butter in the pan. When the butter begins to bubble but not burn, toss in the mushrooms. Saute until the mushrooms are golden brown and push them to the side.
Dry the halibut with paper towels and season both sides with salt and pepper. Place the presenting side down. Cook until the fish turns white about halfway up and turn over.
Finish cooking until the fish is 140 degrees F internally. Remove and set aside.
Turn the heat up to high and add the wine to deglaze the pan.
Turn the heat down to the lowest temp and let it cool down some.
Add the butter to the pan and cook until melted.
Top the fish with the wine and butter sauce and mushrooms.