Combine the cranberries and water in a small saucepan over medium heat
Cook until the cranberries pop and the liquid bubbles
Use a spatula to smash and break up the berries
Once the berries have all popped, remove from heat
Press the cranberries through a strainer into another bowl
Be sure to scrape all of the puree on the underside of the strainer into the bowl as well
Pour the cranberry puree back into the saucepan and set aside for a moment
Whisk the egg yolks and egg together until combined
While whisking, pour in the sugars and whisk until lighter in color
Whisk a small amount of the cranberry puree into the egg mixture to temper the eggs
Add the egg mixture to the cranberry puree in the saucepan, and continue whisking until well incorporated
Place over medium heat, whisking constantly, until the mixture thickens and can coat the back of a wooden spoon, about 8-10 minutes
Remove the pan from the heat, and stir in the butter, one tablespoon at a time.
Strain, again, into a bowl to remove any lumps that may have been created
Cover surface with plastic wrap and chill in the refrigerator for at least one hour or pour into glass jars and allow to cool, then refrigerate