Roll out the pastry to a 35cm circle on a lightly floured work surface, then put onto a baking-paper-lined baking tray. Spread the pistachio paste over the base, leaving a 6cm border around the edge. Chill.
For the filling, put the sugar and shelled pistachios in a small food processor and whizz until the nuts are finely ground. Tip into a large bowl with the ground almonds and butter, and beat with a wooden spoon until pale and smooth. Beat in the eggs then the lemon zest, vanilla and a pinch of salt. When the frangipane is light and smooth, briefly stir in the flour.
Scatter the cherries over the pastry and add dollops of the frangipane, until all the fruit and nutty filling is used up. Fold the border of the pastry up and over the edges of the filling to roughly seal it in. Chill for 2 hours.
Heat the oven to 200C/fan 180C/gas 6 and put a baking sheet on a middle or high shelf. Lightly dust the galette with icing sugar and carefully lift it, on its paper, onto the preheated baking sheet, and bake for 40 minutes until the pastry and frangipane are golden and crisp. Serve hot, warm or cold, with a little more icing sugar, the chopped pistachios and something creamy on the side, such as crème fraîche.
