Combine Bourbon and lemon juice in a cocktail shaker with ice, shake at least 10 times until very cold to the touch. Set aside.
Divide the peach jam, mint leaves, lemon slices and simple syrup into two chilled glasses and muddle gently to bruise the leaves and mix the ingredients.
Fill the glasses with ice and add the bourbon and lemon juice mixture; stir well.
Top with the chilled ginger beer, stir briefly and garnish with a peach slice and mint leaves.