Peach or Blueberry Cream Pie

This came from my Grandma Ann.  She always made it with blueberry pie filling, which is delicious!  I decided to try it with some peaches I had.  The result was really yummy!!
 
1 pie crust, baked as directed (a graham cracker crust can be substituted)

Filling:
1 8 oz. cream cheese, softened
3 cups powdered sugar
1 teaspoon vanilla
8 oz. cool whip
Beat the cream cheese, slowly add the powdered sugar.  Mix in the vanilla.  Fold in the cool whip.  Spread into cooled crust. 

Pie Filling:
Make a paste of:
3 tablespoons cornstarch
1/3 cup water

In a medium saucepan, put:

2 cups blueberries or peaches (chopped)
1 teaspoon lemon juice (only if using peaches)
3/4 cup sugar

Add the paste mixture.  Stir over medium-low heat and cook, stirring constantly to prevent sticking, until thick.  You may need to lower it to low.

Spread the cooled pie filling over the cream filling.  Refrigerate until cold through (2-4 hours).