Combine the ingredients in a shaker and shake to emulsify the egg. Add ice and shake vigorously. Strain into a chilled coup glass. Dot the foam with the bitters.
*For the syrup combine 1 cup sugar, 1 cup water and 1 cup roughly chopped dried chilies in a sauce pan. Heat to a boil and reduce heat to a simmer. Simmer until sugar is dissolved, stirring occasionally. Allow to cool and strain through cheesecloth.