Drain the peach halves on a sieve. Cut 4 halves into slices, puree the remaining peaches together with the peach liqueur. Whip the cream until stiff. Let the vanilla ice cream thaw a little.
Arrange the peach slices on four plates in a fan-like fashion. Form 4 large ice cream balls with an ice cream scoop and place them in the peach slices. Pour cream into a piping bag with a perforated spout and squirt two thick cream patches onto each plate.
Pour peach puree over the ice cream and serve immediately sprinkled with pistachios.