Bring cinnamon sticks, ginger, cloves, pomegranate juice, and sugar to a boil in a medium saucepan. Cook until reduced to 1½ cups, about 40 minutes. Strain syrup through a fine-mesh sieve into a heatproof measuring glass; discard solids. Let cool.
To serve, pour 1 oz. pomegranate syrup and 1 oz. Scotch, if using, into a tall ice-filled glass. Top off with club soda and stir to combine; garnish with a lemon twist.
Do Ahead: Syrup can be made 10 days in ahead. Chill in an airtight container.
