Preheat the oven to 325°F and grease a square baking dish or line one with parchment paper. Place the diced apples in a large bowl, and toss with 1 teaspoon of the cinnamon and the lemon juice, and set aside.
In a separate medium bowl, add flour, baking powder, salt, cinnamon and nutmeg, and mix to combine well, then set aside. In another separate large bowl add the sugar, eggs and vanilla, mixing or beating to combine well after each addition. Add the dry ingredients to the wet ones and mix well to combine.
Scrape about two-thirds of the batter into the bowl of apples, and mix to coat all of the apples in the batter. It will be very chunky. Scrape the remaining one-third of the cake batter into the prepared cake pan and spread into an even layer with a spatula. Scrape the chunky apple-packed cake batter on top of the first layer and spread out evenly.
Cover the pan tightly with foil, and place in the center of the preheated oven. Bake for 20 minutes. Remove the foil, and bake for another 20-25 minutes, or until the center is set. Remove from the oven and allow bars to cool in the pan for at least 10-15 minutes before slicing.