Place cranberries in a medium saucepan. Add water and sugar and bring to a boil over medium heat. Reduce heat to medium-low and cook, stirring occasionally, until cranberries have burst, 8 to 10 minutes.
Pour cranberry mixture into a food processor or blender; blend until smooth, 10 to 20 seconds. Reserve ⅓ cup and return remaining cranberry mixture to the saucepan over low heat.
Whisk egg yolks together in a small bowl. Slowly add reserved cranberry mixture, whisking constantly. Slowly whisk egg-cranberry mixture back into the saucepan and continue whisking until thickened and the curd coats the back of a metal spoon, about 5 minutes. Add butter, 1 tablespoon at a time, whisking until melted and fully incorporated.
Pour into a sterile jar and allow to cool. Curd keeps in the refrigerator for up to 1 week.