How to Make It
Preheat oven to 350°F. Brush a 9-inch round cake pan with oil and line bottom with parchment paper; brush with oil and sprinkle with granulated sugar.
Whisk flour, salt, baking powder, and baking soda in a large bowl.
Pit and roughly chop 2 nectarines. Puree in a blender or food processor until smooth.
Whisk granulated sugar, eggs, and vanilla in a large bowl. Whisking constantly, gradually add ½ cup oil. Add flour mixture in 2 batches, whisking until evenly incorporated. (Batter will be thick.) Fold in nectarine puree and pour batter into prepared pan.
Bake until cake is golden and pulls away from sides of pan, 28 to 30 minutes. Let cool in pan for 10 minutes. Remove cake from pan and transfer to a rack to cool completely. (Cake can be made up to 2 days in advance. Wrap tightly and store at room temperature.)
To serve, dust cake with powdered sugar. Slice remaining 2 nectarines and toss with flaky salt and remaining ¼ cup oil. Serve cake with nectarines and a drizzle of oil.