Pat the halibut dry with a paper towel, and then season both sides with salt and pepper.
Warm the oil and 1 generous tablespoon of the butter in a large skillet set over medium heat. When the butter melts and its foam subsides, sear the fish until attractively browned -- about 45 seconds per side. Transfer the fish to a plate and set aside.
Melt another tablespoon of butter in the skillet. Then add the mushrooms and a sprinkling of salt and pepper. Sauté the mushrooms until they color -- 4-5 minutes. Then stir in the lemon zest, lemon juice, and wine. Let the wine bubble in the skillet for just 1 minute.
Add the spinach leaves. Cover the skillet, lower the heat, and let the leaves wilt for just 1 minute. Then lightly dust the leaves with salt and pepper.
Briefly stir the ingredients (the leaves will continue to wilt), and then push them to the sides of the pan to make an opening in the center. Melt the remaining tablespoon of butter in the opening, and then return the fillets to the pan, on top of the butter. Cover the skillet and cook just until the fillets are cooked through -- about 2 minutes.
Divide the works among 2 plates and enjoy while hot!