Preheat your oven to 300 degrees F.
In a large bowl, cream the butter and sugar together until smooth. Add the vanilla, and the cornstarch/milk mixture, and beat until well-mixed.
In a smaller bowl combine the flour, baking powder, salt, and cornstarch. Stir this into the wet ingredients and combine well.
Begin rolling the cookie dough into balls of about 3 tbsp. each and place on an ungreased baking sheet. Using the bottom of a glass, press down on each ball until they are about an inch thick.
If you would rather roll out the dough and use cookie cutters to cut out shapes, sprinkle flour on a flat surface and use a rolling pin to roll out.
Combine 2 tbsp. cinnamon and 4 tbsp. sugar and sprinkle over cookies.
Place cookies on an ungreased cookie sheet. Bake for 12 - 14 minutes, and no more. The cookies should still seem very soft when you remove them from the oven. Let cool on the pans for about 10 minutes, and then transfer to a wire baking rack and let cool completely.
Allow the ice cream to soften slightly. Spread it into an even layer about an inch think in a pie plate. Put it back into the freezer to set while making the cookies.
Once the cookies are cool take the ice cream out of the freezer and using the same size cookie cutter, cut circles out of the ice cream. Lift them out using a small spatula and place the ice cream circle between two cookies. Press down slightly and wrap in wax paper. Put into an air tight container or ziplock bag in the freezer. Continue until all cookies and ice cream are used.
by The Savvy Kitchen