To make the infused vodka, place the sumac in a large glass or ceramic bowl and pour over the vodka. Cover and set aside for 2 hours, stirring from time to time, then strain back into the bottle through a fine-mesh or muslin-lined sieve.
When ready to serve, place all the ingredients in a shaker with some cubed ice. Shake really hard for 10 to 15 seconds, then double-strain (through a strainer and into a fine-mesh sieve) into two chilled glasses. Serve at once, with a sprinkle of sumac on top.