To make the simple syrup, combine all ingredients in a small saucepan. Bring the mixture to a boil over medium-high heat. Once the sugar is dissolved, remove from heat and cover. Let steep for 20 minutes.
Drain out cinnamon sticks and whole cloves. Set syrup aside to cool to room temperature.
In a cocktail shaker, whisk together rum, orange juice, syrup, and egg.
In a separate small saucepan, heat beer until steaming. Do not let it reach a boil.
Slowly add beer to the cocktail shaker mixture, whisking quickly as you pour it in so the egg doesn't cook.
Pour the mixture back and forth between the cocktail shaker and saucepan until it is nice and frothy.
Pour into a heat safe mug and garnish with freshly grated nutmeg.