In a shaker combine all ingredients except bitters, add ice and shake vigorously. Crack shaker and strain out ice, then shake again (this is for the egg to fluff). Strain into a coupe glass and add bitters.
* To make spice-infused simple syrup, bring 1 cup sugar, 1 cup water, 1 cinnamon stick and 2 whole cloves to a boil in a small saucepan. Reduce heat and simmer 5 minutes. Remove from heat. Let cool completely. Remove cinnamon and cloves and pour through a sieve into a bowl. Syrup can be refrigerated in an airtight container up to 1 month.