In a large bowl, mix together 1/2 cup white sugar, 1/2 cup brown sugar, 2 tablespoons flour and cinnamon. Stir in sliced apples until coated with sugar mixture. Stir in 1 cup cinnamon chips. Pour filling into prepared pie crust, and dot with 3 tablespoons butter.
To make streusel topping: mix together 3/4 cup flour and 3/4 cup brown sugar in a mixing bowl. Cut in 6 tablespoons butter until mixture resembles coarse crumbs. Stir in remaining 2/3 cup cinnamon chips. Sprinkle streusel topping over apple filling.
Bake in preheated oven for 10 minutes, then reduce heat to 350 degrees F (175 degrees C) and continue baking for until filling is bubbling and streusel is golden brown, 35 to 40 minutes more. Allow to cool for at least 1 hour before serving.
While the pie is cooling, prepare the vanilla sauce. In the top of a double boiler over medium heat, whisk together eggs, half-and-half and 1/2 cup sugar. Cook, stirring constantly, until sauce has thickened. Remove from heat, and stir in vanilla. Spoon sauce (warm or cooled) over slices of pie.