Peel and slices the peaches into 1/2" wedges, place in a wide saucepan.
Add the butter to the peaches and cook on medium heat until the butter has completely melted, about 2-3 minutes. Add the key lime juice.
In a medium bowl, mix the sugars, salt, and cinnamon and add to the peaches mix, allow the sugar to melt.
Reduce heat to simmer and let the peaches mix to cook for about 15 minutes while stirring occasionally until the mix has been thickened.
Remove mix from the stove and let cool for about 10 minutes.
Process peaches using a food processor with heavy cream until completely smooth.
Pour mix into popsicles molds and freeze for 6-12 hours.