For cinnamon syrup, bring all ingredients to a boil over medium heat.
Reduce heat to medium-low and let simmer for 8-10 minutes until the sugar has dissolved, stirring frequently.
Remove from heat and let cool. Discard cinnamon sticks, strain into a clean glass jar and cover. Store refrigerated for up to 2 weeks.
For the cocktail, pour Gin over cubed ice. Add fresh lime juice, cinnamon syrup and cloudy apple juice.
Garnish with an apple fan of 3 slices and add grated nutmeg on top (optional).