In a small saucepan, bring the sugar, water, and cinnamon stick to a boil.
Reduce heat to a simmer and cook, whisking occasionally, until the sugar has completely dissolved.
Remove the saucepan from heat, discard the cinnamon stick, and allow the syrup to cool to room temperature.
Place the red wine and orange zest in a large, freezer-safe bowl (not nonstick). Whisk in the cooled syrup.
In the bowl of a stand mixer fitted with a whisk attachment or another large bowl, beat the egg whites just until soft peaks form.
Fold the beaten egg whites into the red wine until evenly blended.
Cover the bowl with freezer-safe plastic wrap and transfer to the freezer.
Every hour for four hours (four times), remove the bowl from the freezer and whisk to break up and blend back together the mixture, especially along the bottom and sides of the bowl. Return the bowl to the freezer.
Allow the mixture to continue to freeze for another hour to overnight.
Before serving, use a fork to stir and blend the mixture again to create a light and fluffy texture.
Serve immediately from the freezer in chilled dessert bowls, with an orange peel strip and fresh mint leaves to garnish.