Place fine strainer over a bowl. Pour the cranberry mixture into the strainer and press with the back of a spoon, extracting as much juice as possible. Discard the solids. Return the strained cranberries to the saucepan with the sugar and cook over medium heat, stirring, until the sugar has dissolved fully. Whisk about 2 tablespoons of the warm cranberry mixture into the egg yolks, then add the egg yolk mixture to the pan. Continue to cook, stirring constantly, until the mixture thickens, about 4-5 minutes. Remove from the heat and whisk in the butter - whisking until the butter is melted and the mixture is fully combined. Pour the mixture into a bowl, cover with a piece of plastic wrap, pressing the plastic wrap directly onto the surface, and refrigerate until cold, about 1 hour.