Add 1 shot of rum and 2 tablespoons of Caramel Sauce to bottom of 4 heatproof glass mugs. Divide the coffee evenly between the mugs and top with a large dollop of whipped cream.
In a medium saucepot combine sugar, 3 tablespoons water, and lemon juice. Heat over medium-high heat. When sugar turns amber in color carefully and slowly whisk in heavy cream. Remove from heat and let cool. Place in airtight container and store in refrigerator for up to 3 weeks.
In a small bowl whisk together 2 tablespoons water with the cornstarch. In a small pot over medium heat reserved peach juice, cornstarch mixture, brown sugar and salt. Once the sauce thickens, about 5 minutes, stir in the chopped peaches.
In a chilled mixing bowl whip heavy cream with confectioners' sugar until soft peaks form. Use 1 cup for mug pies, and reserve the rest for another use.
Begin assembling peach pies by in clear glass mugs. Place a layer of graham crackers at the bottom, then a big spoonful of the peach pie filling. Sprinkle with another layer of graham crackers. Top with a scoop of vanilla ice cream, then another layer of graham crackers followed by a dollop of whipped cream.
To make a kid friendly version, omit rum and substitute the coffee with milk.