Preheat oven to 450°F.
Season Halibut with salt and pepper.
In an ovenproof skillet on medium-high heat, heat the vegetable oil. Add the halibut, skin side down and sear until golden brown. Turn the fish over and place the skillet in preheated oven for 3 to 4 minutes. When done, the fish should be flaky and moist. Remove from the oven and keep warm.
In a saucepan over medium-high heat reduced white wine, shallots, and rice wine vinegar to syrupy consistency. Strain. Return liquid to a clean saucepan and place on low heat.
To ensure sauce will not split, add ½ tbsp cream to help stabilize the sauce. Slowly whisk in butter cut by cube, do not boil or sauce will separate. Season the sauce with salt and lemon juice. Keep warm.
In a non-stick fry pan over medium heat, heat butter. Add mushrooms and sauté. Season with salt and pepper. Add asparagus to reheat.
Place mushrooms and asparagus in the centre of a large plate. Place a piece of halibut on top and spoon sauce over fish until nicely coated.