Slice the dried apricots in half. Rinse them with water. Place them in a sauce pan with the water, bring to a boil and cook for 5 minutes.
Combine the cornstarch with the orange liqueur and about 1 tablespoon of the apricots' cooking liquid. Mix until smooth then stir into the cooked apricots. Add the white sugar and combine. Pour mixture into the unbaked pie shell and seal with the top crust. Brush milk over top crust for color, if desired.