Combine the half-and-half, vanilla bean and seeds, and salt in a non-reactive saucepan over medium heat. Bring the cream to the boiling point and scald it. Remove from the heat.
Beat the sugar and egg yolks in a bowl. Add the half-and-half mixture, about 1/4 cup at a time, to the beaten eggs and sugar, whisking in between each addition, until all is used. Pour the mixture back into the saucepan reduce the heat to medium-low, and cook, stirring, for 5 to 6 minutes, or until the mixture becomes thick enough to coat the back of a spoon. Remove from the heat, strain through a fine mesh sieve and cool completely (allow the custard to cool under refrigeration for at least 2 hours).
While the custard is cooling, prepare the peaches. In a saute pan set over medium heat, add the butter. Once melted, add the ginger to the pan and saute until fragrant, about 30 seconds. Add the peaches and sugar to the pan and cook, stirring occasionally until most of the sugar has evaporated, about 10 minutes. Raise the heat to high and once the pan is hot, remove from the heat and add the bourbon. Quickly return the pan to the heat and ignite the bourbon. Once the flames die out, turn the heat off and allow the peaches to cool. When cooled, fold the peaches into the ice cream custard.
After completely cooled, pour the custard into the ice cream machine and follow the manufacturer's instructions for churning time. Place ice cream in a freezer-safe container and freeze until firm, about 4 hours.
Serve in ice creams cups with the caramel sauce and garnished with fresh sliced peaches and fresh mint leaves.
Combine the sugar, water, and lemon juice in a medium, heavy saucepan over medium-high heat. Cook, stirring, until the sugar dissolves. Let boil without stirring until the mixture becomes a deep amber color, 2 to 3 minutes, watching closely so it doesn't burn. Add the cream, whisk to combine, and remove from the heat. Add the milk, 2 tablespoons at a time, until the desired consistency is reached. Remove from the heat and cool to room temperature before serving. (The sauce will thicken as it cools.)
Yield: generous 3/4 cup