In a medium saucepan, combine the granulated sugar, cornstarch, and salt. Whisk in the cream and cook and stir over medium heat until thickened and bubbly. Remove from heat. Stir in butter, brown sugar, and vanilla until butter melts. Pour into baked pie shell and sprinkle lightly with cinnamon.
Bake, uncovered, in a 325 degree F oven for 30 minutes (center of pie will not be set). Cool on a wire rack 1 hour. Chill 3 to 6 hours before serving (pie will set up upon chilling); cover for longer storage.