Bring juice and sugar to a boil in a 2-qt. saucepan over medium-high heat. Whisk in farina, reduce heat to medium-low, and cook, whisking constantly, until thickened, about 5 minutes. Transfer to the bowl of a stand mixer fitted with a whisk, and process on medium-high until thick and doubled in volume, about 12 minutes. Serve in bowls with milk poured over top, if desired.