In a medium saucepan combine 2 cups half and half, vanilla bean paste, sugar, salt and cinnamon stick and bring to a simmer over medium heat.
Combine cornstarch with remaining 1/2 cup half and half and whisk together until there are no more lumps.
Add cornstarch mixture to saucepan and continue to cook for about 5 minutes until mixture begins to thicken, stirring often. Do not boil.
Reduce heat to low and continue to cook for 5 more minutes.
Remove cinnamon stick.
Stir in butter.
Pour mixture into a 1-quart dish covered with plastic wrap and refrigerate until chilled, about 3 hours.
Heat oven to 350 degrees.
Line a large baking sheet with parchment paper.
Beat butter, brown sugar and granulated sugar in a large bowl until creamy.
Add egg and vanilla and continue to beat until well combined.
In a medium bowl sift together flour, cinnamon, baking soda and salt.
Add flour mixture to butter mixture. Mix well.
Add oats and raisins and stir until well combined.
Drop by tablespoonfuls onto prepared baking sheet.
Bake 10 minutes or until golden brown.
Cool on wire racks.
To assemble parfaits place 1 1/2 cookies, crumbled into bottom of glass, top with some pudding, then top with another 1 1/2 cookies. You will have extra cookies.