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