Add all ingredients into a shaker and dry-shake (without ice) until frothy.
Add ice and shake again until well-chilled.
Strain into a cocktail glass.
Garnish with a sprinkle of ground cayenne.
*Ginger syrup: Bring 1 cup sugar and 1 cup water to boil in small saucepan. Add 4 oz peeled ginger cut into thin rounds (about a 10-inch long piece). Remove from heat and allow to steep for 30 minutes, then strain out solids. Store in refrigerator up to several weeks.