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In a blender, combine the butternut squash, milk, and cream. Pulse to combine, and blend for 30-45 seconds. Reserve for later use.
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In a bowl, whisk together the egg yolks and corn starch, reserve.
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In a heavy-bottomed pot, whisk together the sugar, water, and salt, and place over medium heat on the stove. Without stirring further cook the sugar mixture for 5 minutes. Slowly add the milk and cream mixture to the sugar, whisking constantly. Do the slowly as the mixture will pop and bubble as you do this. Bring the mixture to a boil.
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Drip by drip, drizzle in 1/2 a cup of the boiling mixture into the whisked egg yolks and cornstarch. Whisking constantly so the eggs don’t scramble, this is a temper of the eggs. Reduce the heat on the milk mixture to low and whisk in the eggs. Continue whisking for 1 minute as the mixture becomes thick. Remove from the heat and whisk in the butter and vanilla.
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Pour the mixture into the serving glasses or bowls. Fill 6, 6oz bowls halfway and cover tightly with plastic wrap touching the top of the pudding to prevent a skin from forming. Refrigerate for 4-6 hours, or overnight until chilled and thickened.
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Make the whipped cream by beating the heavy cream and powdered sugar together until thick and creamy, fold in the vanilla.
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To serve, top each bowl with a couple of tablespoons of caramel sauce and a dollop of whipped cream.