Penicillin Cocktail with Ginger, Lemon and Honey

Name: Penicillin Cocktail with Ginger, Lemon and Honey
Prep time: 15 min
Total time: 15 min
Cuisine: American
Ingredients: 1 1/2 ounces Scotch whiskey* (3 tablespoons); 3/4 ounce freshly squeezed lemon juice (about 1/2 lemon, 1 1/2 tablespoons); 1/2 ounce ginger syrup (1 tablespoon); 1/2 ounce honey syrup (1 tablespoon); 1 sprig rosemary, for garnish (optional); 12 ounces ginger** (350 grams, or to yield 1/2 cup, 125 milliliters, of juice); 1/2 cup sugar (100 grams); 3/4 cup honey*** (255 grams); 1/4 cup hot water (60 milliliters)