1. In a large saucepan bring 1 3/4 cups water and sugar to a boil over medium-high heat; cook, stirring, until sugar is dissolved. Remove from heat and let cool to room temperature.

2. Transfer sugar mixture to a large container. Add 8 1/2 cups water, lemon juice, rum, Cognac, whiskey, peach brandy, apple juice, and bitters; stir to combine. Add a large block of ice. Let stand in a cool place for 1 hour before serving.

3. Serve punch in rocks glasses over ice; garnish with a lemon slice if desired.