Blanch the peaches, and remove from the heat. Peel, halve, remove the seeds, and chop. Bring to a boil with 800 ml (approximately 27 ounces) of orange juice, and sweeten to taste. Mix the cornstarch with a little water until smooth. Add to the cooking liquid, and thicken briefly. Divide into glasses, then chill in the refrigerator.
Beat the cream with the powdered sugar and a pinch of cinnamon until stiff. Garnish each of the gazpachos with a dollop of the cream and a pinch of cinnamon, then serve.