Line a large baking sheet with waxed paper.
Using a 1/4-cup ice-cream scoop, scoop out 1 serving vanilla ice cream. Using the handle of a wooden spoon, make an indentation in the center. Fill with a cherry and a few of the coarsely chopped cookie pieces. Smooth over with spoon. Invert onto prepared baking sheet. Repeat to make 3 additional vanilla tartufos. Sprinkle generously with finely chopped pistachio nuts. Freeze.
Repeat step 2 using chocolate ice cream and filling each scoop with remaining coarsely chopped pistachio nuts and cherries. Place on the prepared baking sheet and sprinkle generously with the finely chopped chocolate wafer cookies. Freeze all for at least 8 hours or overnight.
To serve, drizzle chocolate syrup onto 8 dessert plates. Cut tartufos in half or quarters and place on plates.