Transfer mixture to the bowl of an ice cream maker and follow manufacturer's directions. Churn the mixture until the ice cream reaches a soft-serve consistency.
Add a layer of the ice cream to the bottom of a freezer-proof container. Distribute a layer of the streusel on top. Add a layer of the prepared quince on top of the streusel. Repeat the layering until you have used all the ingredients.
Place the container in the freezer for two hours or until it hardens. Scoop and serve.