How to Make It
Grind mastic gum pieces and a pinch of sugar in a mortar and pestle until finely ground. Whisk together ground mastic gum mixture, 1 cup milk, and cornstarch in a small bowl until dissolved.
Whisk together cream, 3/4 cup sugar, and remaining 3 cups milk in a large, heavy saucepan. Bring to a simmer over medium. When milk mixture is about to boil, add mastic mixture, and cook, whisking constantly, until thickened, about 1 minute. Remove from heat.
Carefully ladle hot pudding into 12 (6- to 8-ounce) heatproof dessert bowls or glasses. Press plastic wrap or wax paper directly onto surface of each pudding to prevent a skin from forming. Let cool slightly, about 20 minutes; refrigerate until set and chilled, at least 2 hours or up to 24 hours.
Meanwhile, combine cranberries, 1/4 cup water, and remaining 1/2 cup sugar in a small saucepan. Cook over low, stirring occasionally, until cranberries burst and release their juices, 8 to 10 minutes. Remove from heat, and let cool. Cover and chill until ready to serve.
Serve puddings cold, topped with cranberry sauce.