Preheat the oven to 425ºF. Lightly brush the top of the pita with olive oil, reserving a little, then spread the jam on top, not getting too close to the edge, as the jam will run a bit. Sprinkle pistachios on top and gently brush tops of nuts with the remaining olive oil, to prevent burning.
Place on a baking sheet and bake 5 - 10 minutes, or until jam is bubbly and pistachios are turning golden brown. Remove from oven and let cool a few minutes before slicing into four pieces with a pizza cutter.