Preheat the oven to 350 degrees F. Grease a 9-inch springform pan with butter and line bottom with parchment.
Whisk together the flour, baking powder and salt in a small bowl.
Cream the brown sugar and butter in a stand mixer fitted with the paddle attachment for 6 to 7 minutes; the mixture will lighten and double in volume. Add the eggs one at a time, beating after each addition until combined. Beat in the vanilla extract. Add the flour mixture and beat until just combined. Fold in the apple pieces.
Pour the batter into the prepared pan. Bake until golden brown and a toothpick inserted into the center of the cake comes out clean, about 1 hour.
Cool the cake in the pan for 30 minutes, then remove the sides of the pan. Brush the cake with the maple syrup and sprinkle with the orange zest and toasted pistachios.