Heat the oven to 400 degrees. Grease a 9 x 13-inch baking pan, then line with parchment paper (base and sides). Set aside.
In a stand mixer, beat the butter and sugar in the bowl with the paddle attachment, on medium speed for 2 to 3 minutes, until pale and creamy.
With the mixer running on low speed, add the eggs, one at a time, until each egg is incorporated.
In a separate bowl, mix the sifted flour, baking powder, salt, and ground pistachios together until mixed. Using a metal spoon, fold the dry mixture into the wet mixture until incorporated.
Carefully fold the cherries into the mixture until evenly distributed, then pour the batter into the prepared pan.
Bake the cake for 25 to 30 minutes, until golden brown and a toothpick inserted into the center comes out clean. Let cool completely in the pan, then cut into 16 equal pieces. Serve with ice cream. a few fresh cherries and a dusting of powdered sugar.