Preheat the oven to 375°F. Lightly grease a 9-inch springform pan or round cake pan. In a large bowl, whisk together 1 cup flour, the baking powder and salt.
In a small bowl, toss together the remaining 2 teaspoons flour, ½ cup brown sugar, chocolate chips, walnuts and cinnamon.
In another small bowl, whisk together the eggs, granulated sugar and remaining ¼ cup brown sugar until smooth. Whisk in the oil and vanilla. Stir into the flour mixture until just combined. Pour half the batter into the prepared pan, and top with half the apples and half the chocolate chip mixture; repeat with the remaining batter, apples and chocolate chip mixture. Bake the cake until a toothpick inserted in the center comes out clean, about 45 minutes. Let cool in the pan set on a wire rack.