Gently wash the peaches to remove any fuzz, being careful not to bruise their delicate skin.
In a large saucepan or Dutch oven, combine the red wine, sugar, and cinnamon stick.
Bring to a gentle simmer over medium heat, stirring occasionally until the sugar has completely dissolved, creating a fragrant syrup.
Carefully add the whole peaches to the simmering wine syrup. Ensure they are mostly submerged.
Reduce the heat to low and poach very gently for 8-10 minutes, turning them once halfway through.
Remove the saucepan from the heat and let the peaches steep in the hot wine for 30 minutes. This allows them to absorb the beautiful color and flavor.
Using a slotted spoon, carefully remove the peaches from the wine.
Once they are cool enough to handle, the skins should slip off easily.
Discard the skins.
Arrange the peeled peaches in a beautiful serving bowl or glass container.
Strain the poaching liquid over them to remove the cinnamon stick.
Chill in the refrigerator for at least 1 hour before serving. The flavors will meld and deepen as they cool.