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In a medium saucepan heat milk, cream, sugar and coffee powder until just about to boil.
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Whisk egg yolks together in a heatproof bowl.
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Slowly pour the cream mixture into the yolks whisking quickly to temper the eggs.
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Scrape the tempered mixture back into the pan and reheat stirring occasionally until the mixture thickens a bit, coating the back of a wooden spoon.
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Remove from heat and strain into a clean heatproof bowl.
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Cover with plastic wrap, making sure the wrap touches the top of the mixture to prevent a skin from forming on top.
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Refrigerate for at least 3 hours or overnight.
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Transfer mixture to the bowl of an ice cream maker and follow manufacturer's directions to mix.
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When ice cream reaches soft serve consistency, add in the cake scraps.
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Transfer the ice cream to a container and place in freezer until it hardens.