Preheat oven to 400 degrees Season Filet Mignons with salt and pepper and sear quickly in 2 tablespoons of butter and 1 tablespoon olive oil. Cool. Melt 6 tablespoons butter and remaining olive oil in a skillet over medium heat. Add mushrooms and saute, stirring, until they release their liquid. Add Madeira and chives and cook over medium-low heat until soft. Season with salt and pepper to taste. Cool.
Melt remaining butter. Cut phyllo sheets into thirty six 8 1/2-inch squares. To make parcels: Place one phyllo square on flat surface, brush with butter, place another square on top of first with corners turned 45 degrees. Continue in this way, turning each square before placing on top of the other so the corners do not lay on top of one another. Each parcel should contain 6 sheets of phyllo. Keep phyllo covered as you're working so it doesn't dry out. Spoon 2 tablespoons of mushrooms into center of each packet. Place tenderloin on top of mushrooms. Top tenderloin with another 2 tablespoons of mushrooms.
Gather edges of phyllo together and gently twist. Tie with a leek ribbon. Transfer to parchment-lined baking sheet, brush lightly with melted butter and bake approximately 20 minutes, or until beef registers 125 degrees (medium-rare) on an instant read thermometer (insert through the center of the packet).