Keep the individual serving plates in the oven at the lowest setting so they are warm when you serve.
Pat-dry the haddock fillet then set aside.
Heat the oil and half of the butter in a frying pan over medium heat. Add the slivered almonds and sauté until they are golden, paying attention not to let them burn. Take the almonds out of the pan and keep them warm on a plate in the oven.
Add the remaining butter to the pan, then add the haddock and sauté over fairly high heat, 2-3 min on each side. Pour in the wine, then lower the heat, cover, and cook 7-10 min, depending on the thickness of the fillet. Check with a fork to see if it is cooked through.
Add salt and pepper to taste, then cover the fish with the almonds and serve on the warmed plates.