Heat milk, cream, sugar, and coffee powder in a saucepan until just about to boil.

Whisk egg yolks together in a heatproof bowl.

Slowly pour the cream mixture into the yolks whisking quickly to temper the eggs.

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.

Remove from heat and strain into a clean heatproof bowl.

Cover with plastic wrap, making sure the wrap touches the top of the mixture to prevent a skin from forming on top.

Refrigerate for at least 3 hours or overnight.

Transfer mixture to the bowl of an ice cream maker and follow manufacturer's directions to mix.

When ice cream reaches soft serve consistency, add in the cake scraps.

Transfer the ice cream to a container and place it in the freezer until it hardens.