In a large bowl, add sugar & lemon peels, and rub together to release the citrus oils into the sugar. (This is called oleo-saccharum.)
Allow oleo-saccharum to infuse for at least 30 minutes.
Dissolve sugar with warm water.
Add rum, cognac, lemon juice, and peach brandy; stir to mix.
f you want to serve the punch cold, add a block of ice to chill, and continue to add smaller pieces of ice for desired dilution.
Serve in a punch glass, and garnish with lemon wheels and freshly grated nutmeg.