Place half-and-half and the heavy cream into a saucepan, and heat over medium heat. Bring the mixture just to a simmer, stirring occasionally and remove from heat.
Next, in a medium bowl whisk the egg yolks until they lighten in colour, then gradually whisk in the sugar. Now temper the cream mixture by gradually adding small amounts of the heated cream, until ⅓ has been added. Finally pour in the remainder and return the entire mixture to the saucepan. Continue to cook over low heat, stirring constantly, until the mixture thickens slightly and coats the back of a spoon, reaching 170 to 175 degrees F.
Next pour the cream and egg mixture into a large bowl and cool at room temperature half an hour. Stir in the vanilla, and the inside scraping of the vanilla bean (or omit the vanilla bean and use 2 teaspoon of vanilla extract). Refrigerate the mixture 4-8 hours until the temperature is 40 degrees F or below.
Pour the mixture into your ice cream maker and follow the manufacturer’s direction to churn ice cream. Meanwhile, chop the kit kat bars into small pieces. Finally during the last 5 min as you churn in the ice cream maker, add in the chopped kit kat pieces. Enjoy from the ice cream maker as soft serve or freeze 3-4 hours in the freezer in an air-tight container for the ice cream to fully harden