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Make the chocolate pudding: in a medium saucepan, combine the cornstarch and sugar; whisk in ½ cup half-and-half until the mixture is smooth.
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Add in the remaining ¾ cup and bring to a boil, whisking constantly.
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Continue to cook mixture over med-high heat, whisking, until the mixture thickens, about 3-4 minutes.
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Take the pan from the heat and whisk in the chocolate and butter; continue to whisk until all the chocolate and butter have melted and the pudding is very smooth; stir in the vanilla.
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Scrape the pudding into the prepared pie crust and smooth the top with a rubber spatula.
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Make the butterscotch putting: in a medium saucepan, combine the butter, brown sugar, and salt; cook the mixture over low heat, whisking, until the butter is melted and the sugar is dissolved.
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In a mixing bowl, combine the cornstarch and ½ cup of half-and-half; whisk to dissolve; set this mixture aside.
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Add the remaining 1 ½ cups half-and-half to the saucepan; whisk until it is combined with the brown sugar mixture.
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Add in half-and-half/cornstarch mixture to the pan; stir to combine, and turn the heat to med-high; cook, whisking, until the mixture thickened, about 3-4 minutes.
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Scrape the butterscotch mixture into the pie shell and smooth the top layer of the pudding with a rubber spatula so that it evenly covers the chocolate pudding.
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Place plastic wrap directly on the surface of the filling and refrigerate the pie until the filling is completely set, about 6 hours and up to 1 day.