Step 1

Lightly butter and flour a 9-inch springform pan. Or simply line the pan with parchment paper instead. (You can use a cake pan if you don’t have a springform pan; but if you do so, leave an overhang with the parchment paper so you can easily lift out the cake.)

Step 2

In a food processor, combine the pistachios and 1 tablespoon granulated sugar and pulse until they are a beautiful green sandy texture. Add the butter and remaining sugar and pulse until fully incorporated. Add the egg, buttermilk, and vanilla, and pulse again, scraping down the sides once or twice with a rubber spatula, until the mixture is smooth.

Step 3

In a medium bowl, whisk together the flour, baking powder, and kosher salt. Add half of the flour mixture to the batter and pulse a few times. Add the remaining flour mixture and pulse just until smooth. Scrape the batter into the prepared pan and smooth out the surface with the spatula. Lightly press the plums into the batter and place in the fridge to chill for 30 minutes.

Step 4

Preheat the oven to 350 degrees F.

Step 5

Scatter the turbinado sugar over the batter. Bake the cake until the edges are deeply golden brown and a paring knife inserted in the center comes out clean, 45 to 50 minutes. Set the pan on a wire rack to cool for 5 minutes before slicing and serving.