Place cranberries, sugar and 1 cup of water into a large saucepan/dutch oven
Place diced apples, nutmeg, cinnamon and 1 cup of the apple cider in a medium-sized saucepan.
Cook the cranberry mixture over medium-high heat until water boils and cranberries burst open. Simultaneously, cook the apple mixture on a separate burner over medium-high heat, stirring occasionally, until apples are softened.
Add the cooked apple mixture into the cooked cranberry mixture and leave the burner on medium-high heat.
Mix the cornstarch with the remaining 1/3 cup of apple cider until completely dissolved. Then, add the mixture in gradually, stirring after each addition, until sauce reaches the desired consistency.
***See Recipe Notes below regarding how cooking/stirring the sauce will affect the texture and consistency.***
Taste test the sauce and add additional sugar, if desired/needed. Serve the sauce however you'd like - hot, room temperature or cold. It's delicious all ways! Store leftover sauce in an airtight container in the refrigerator for up to 1 week.