Place a metal mixing bowl in the freezer to chill for at least 1 hour
Place peeled, sliced peaches into a separate bowl. Sprinkle peaches with 2 teaspoons of sugar, 1 teaspoon of vanilla extract, almond extract, and cinnamon. Stir to combine
Place peach mixture in the refrigerator for 1-2 hours to allow peaches to "marinade" and release juices
Pour heavy cream, 1/2 teaspoon vanilla extract, and 1/2 cup of sugar into the chilled mixing bowl. Using an electric mixer, whip on medium high until reaching a whipped cream consistency
To the whipped cream mixture, blend in the fresh and sweetened condensed milks
Remove peach mixture from the refrigerator and puree in a blender or food processor until desired consistency (smooth or slightly chunky)
Stir the peach puree into the cream mixture until thoroughly combined
Pour into a pan or bowl, freeze for at least 6 hours
Scoop and enjoy!