Prepare pastry for a single-crust pie, or use a refrigerated pie crust. On a lightly floured surface, slightly flatten dough. Roll dough from center to edge into a 12-inch circle. Wrap pastry circle around rolling pin; unroll into a 9-inch pie plate. Ease pastry into pie plate without stretching it. Trim pastry to 1/2-inch beyond edge of pie plate. Fold under extra pastry even with edge of plate. Crimp edge as desired. Do not prick pastry.
Line pastry with a double thickness of foil. Bake in a preheated 450-degree oven for 8 minutes. Remove foil. Bake for 4 to 5 minutes more or until pastry is set and dry. Remove from oven. Reduce oven temperature to 350 degrees.
In a small saucepan combine preserves, cornstarch, the water, and ginger. Cook and stir over medium heat until thickened and bubbly. Spread over bottom of pastry shell.
For filling, in a medium bowl combine eggs, sugar, vanilla, cardamom, and salt. Gradually stir in half-and-half.
Place pastry shell on oven rack. Carefully pour filling into pastry shell. Cover edge of pie with foil to prevent overbrowning. Bake for 25 minutes. Remove foil. Bake for 15 to 20 minutes more or until a knife inserted near center comes out clean. Cool on a wire rack. Cover and chill within 2 hours.
If desired, pipe or spoon whipped cream on pie and sprinkle with additional cardamom.