In a small bowl, combine sugar and cornstarch. In another small bowl, add half-and-half. Stir cornstarch mixture into the half-and-half.
In a medium saucepan, cook half-and-half mixture over medium heat, stirring constantly, until thickened. Stir in vanilla. Remove from heat. Once slightly cooled, place plastic wrap over surface to prevent skin from forming.
On a well-floured surface, roll Sweet Dough into a 13-inch circle; transfer to a 10-inch deep-dish pie plate. Add half-and-half mixture, and fold remaining dough over onto the half-and-half mixture.
Bake until crust is golden brown, about 25 to 30 minutes. Let pie cool to room temperature, then refrigerate 4 hours before slicing.