Preheat the oven to 350 degrees and generously butter a springform pan with softened butter. (I use a lot here, it makes the outside of the cake extra brown and toasty and helps it come out easily.)
Now cream the 1/2 cup butter and 3/4 cups sugar in a stand mixer until fluffy. Add the eggs one at a time until well incorporated.
Add the flour, baking powder, and salt, and mix just until combined. Pour into the prepared pan.
Place in the plums, skin side up (I did the opposite here and it still worked). Sprinkle with the pistachios and a little more sugar.
Bake one hour or until a cake tester comes out clean. Cool in the pan for 15 minutes, then remove the sides, cool completely, and dust with powdered sugar right before serving.