Take about 1/4 cup of the milk and keep it aside.
Put the remaining milk and sugar in a thick walled pan and slowly bring it to boil, stirring frequently to dissolve the sugar. Turn the heat down and allow the milk to simmer for about 2 to 3 minutes.
Slit open the vanilla bean and scrape the pulp inside and add to the milk. Chop the beans into pieces and also add to the milk. Take the milk off the heat and allow the vanilla to infuse into the milk for about an hour.
Strain the vanilla infused milk, to remove the vanilla bean pieces. Return the milk to the thick walled pan and just bring to a boil. Turn down the heat to medium.
Now dissolve the cornstarch in the 1/4 cup milk and add it to the simmering milk, stirring constantly to make sure no lumps form.
Cook just till the milk thickens into a custard and coats the back of the spoon. Take it off the stove and allow it to cool, stirring occasionally to prevent a skin from forming on top.
Add the cream to the thickened milk and whisk by hand till smooth. Pour the ice cream into a flat container and freeze till set.
Take the ice-cream out and break up the crystals by mixing it with a fork or hand held blender till mushy. Freeze till set. Repeat this process of breaking up crystals two more times fro a creamy ice-cream.
After the last time you do this, break the crxe8me cookies into pieces and add this to the ice-cream. Fold it just enough to uniformly distribute the cookie pieces.