In a medium saucepan over medium heat, combine 1/2 cup sugar, 1/2 cup milk, 1/2 cup cream, and 1/4 cup butter. Heat until butter is melted, stirring occasionally. In a small bowl, whisk together the cornstarch, 2 tablespoons milk, and vanilla; stir into saucepan. Cook until thickened, stirring constantly. Remove from heat, and set aside to cool slightly.

Preheat oven to 400 degrees F (200 degrees C). In a medium bowl, combine the apples, flour, and cinnamon. Mix well.

Line a 9 inch pie pan with pie dough. Pour thickened filling mixture into pastry-lined pie pan. Arrange apple mixture evenly over filling. Top with second crust, seal and flute the edges. Cut slits in top crust.

Bake for 30 to 40 minutes, or until crust is golden brown and apples are tender. Cool for at least 30 minutes.

In small bowl, combine confectioners' sugar, 1 tablespoon milk, 1/4 teaspoon vanilla, and 1 tablespoon softened butter. Blend until smooth; pour evenly over warm pie. Refrigerate for AT LEAST 1 1/2 hours before serving (longer is better).