Preheat the oven to 325ºF (160ºC). Grease a 9- or 10-inch (23-25 cm) cake or spring form pan with butter, dust it with flour and tap out any excess. Line the bottom of the pan with a round of parchment paper.
Using a food processor, grind the sugar, pistachio paste, and 1/4 cup (35g) of flour until the almond paste is finely ground and the mixture resembles wet sand. The pistachoi paste is much more liquid than almond paste, so if you're used to a drier mixture at this point, fear not.
In a small bowl, whisk together the remaining 3/4 cup (105g) of flour, baking powder, and salt.
Add the cubes of butter and the vanilla and almond extracts to the sugar mixture, processing until the batter is smooth. It will be still fairly runny and vivid green. It gets better, I promise.
Add the eggs one at a time, processing a bit before the next addition. Scrape the sides down if necessary.
Add half the flour mixture and pulse the machine a few times. Add the rest, pulsing the machine until the dry ingredients are just incorporated. Do not overmix. (You can also transfer the batter to a bowl and mix the dry ingredients in, which ensures that you don’t overbeat it.)
Scrape the batter into the prepared cake pan and bake the cake for about 60 minutes, or until the top is deep brown and feels set when you press in the center.
Remove the cake from the oven and run a sharp or serrated knife around the perimeter, loosing the cake from the sides of the pan. Let the cake cool completely in the pan. It will sink in the middle a little. This is nothing to worry about.
Once it's cool, remove it from the pan. It stays fresh for four days wrapped tight or in a cake dome with parchment paper pressed to the cut side.
This cake is wonderful wiht summer fruit. It woudl also be incredible with a white chocolate pistachio ganache, or a rose and strawberry flavoured whipped cream, or an orange sauce.