Bring the milk, sugar, salt, vanilla and cinnamon stick to a simmer over medium heat in a medium saucepan or Dutch oven. Stir in the orzo and reduce the heat to low, just to maintain a gentle simmer. Cook, stirring often, until the orzo is cooked and the liquid is beginning to thicken slightly, 12 to 14 minutes; there will still be a good amount of liquid. Add the white chocolate chips and orange zest and stir until the chocolate is melted. Allow to cool to room temperature, about 20 minutes, stirring occasionally to prevent a skin from forming over the surface. Discard the cinnamon stick.
Spoon the pudding into serving vessels of your choice and refrigerate until chilled, at least 1 hour and up to overnight. Serve with crushed amaretti cookies sprinkled on top.