To make the simple syrup, mix the water and sugar together in a small pot and let come to a boil over medium heat, stirring occasionally. When the syrup is clear add the pears, cinnamon and nutmeg and let boil for 1 min. Remove from heat and let steep until cool. Strain the simple syrup through a wire mesh sieve. Reserve the pears and discard the cinnamon and nutmeg. Refrigerate both the simple syrup and the pears until cold.

For the cocktails, to a pitcher add the rum, simple syrup, and apple juice, using how much to taste. Refrigerate until ready to use. For each cocktail serve over ice and garnish with a teaspoon of the pears and a cinnamon stick.