Clean your fillets from hard fats and remove what you do not like.
Leave the fillets at room temperature for about 60 minutes and towel them with kitchen towels, removing all the water and possible blood. Before cooking, brush them with some canola oil and season then well with salt.
Heat two tablespoons of canola oil in a non-stick pan on high heat for about a minute. Apply the canola oil all over the pan with rotary movements. Throw the fillets in and immediately, lower the heat to medium. Leave them for about 3 minutes without moving them and preferably without piercing them. Depending on the thickness or the doneness , you can leave it for up to 6 minutes in the pan.
Turn the filet mignon and roast for another 2-5 minutes depending on the thickness and the doneness. Set aside and cover with foil to rest, until the sauce is ready.
Pour the wine into the pan and increase the heat. Let the wine boil for about 10 minutes or till it’s reduced to 3/4. Return any juice from the fillets, if there is any, to the pan. Wait until it stops boiling. Then add the butter, one tablespoon at a time by stirring well until it melts. Add salt and serve over the fillets. Add freshly ground black pepper.