Melt the ½ stick of butter (4 tablespoons) in a saucepan over medium heat. Whisk in the flour. Continue whisking for 2 minutes letting the butter and flour form a paste. Slowly whisk in the milk, cream, sugar, and vanilla. Bring to a boil, lower the heat and let cook for 5 minutes, whisking frequently as the mixture thickens.
Heat the oven to 375 degrees.
Meanwhile, line a 10-inch round cake pan or pie dish with foil, allowing access to hang out of the sides of the pan. Use this later to lift the baked pie out of the pan. Next, using a pastry brush or spoon heavily grease the pan with some of the melted butter avoiding the white milk solids on the bottom.
Place one fillo sheet in the pan. Edges of fillo should hang over edges of the pan. Lightly brush the fillo sheet with clarified butter. Make sure to brush the hanging sides as well. Continue to layer seven more sheets of fillo brushing each layer (and sides) with clarified butter and rotating sheets to cover the pan. You should now have a total of 8 sheets. Make sure you don't soak the sheets with the clarified butter; just lightly brush enough to apply a very thin layer.
Pour the warm filling into the pie crust. Then, continue placing remaining 8 sheets of fillo and brushing with butter in the same manner as the first batch.
With a sharp knife, cut the pie into 8 wedges. Finally, fold the overhanging fillo up over the top of the pie, creating ruffled edges. Cut off excess if necessary.
Bake until golden brown, about one hour. Loosely cover the surface of pie with foil if it's browning too fast while baking.
Let the pie cool before serving.
~ Free Tip ~ You can use a 9-inch ready pie crust instead of the fillo dough for a more traditional pie.