For the Coffee-Anise Syrup: Combine the ingredients in a small saucepan set over medium-high heat, and bring to a boil. Reduce the heat and simmer for 10 minutes. Turn off the heat, and let the ingredients steep for at least 10 minutes or up to an hour. Strain the syrup through a fine sieve, and store in a glass jar in the refrigerator for up to three months.
For the cocktail: Combine all the ingredients in a cocktail shaker. Add a small handful of ice and shake vigorously. Strain the drink into a martini or coupe glass and garnish with a lemon peel.
Recipe by Three Many Cooks at https://threemanycooks.com/recipes/smoke-velvet/