Place your diced apples in a large saucepan with the lemon juice and brown sugar. Cook the apples over medium heat until the apples are soft. Remove from the heat and allow to cool completely.
Preheat your oven to 350 degrees F. Grease 2 9-inch round cake pans or three 8-inch round cake pans, then place a round of parchment in the bottom of each and spray the round. I used 9-inch cake pans.
Combine the flour, baking powder, baking soda, salt, and spices in a medium bowl. Whisk the milk and vanilla together in a small measuring cup. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, 3/4 cups granulated sugar and the maple syrup on medium speed (stopping to scrape down the sides of the bowl once or twice) until light and fluffy, about 4 minutes. Add the eggs one at a time, beating for one minute after eat addition.
Scrape down the sides of the bowl, then with the mixer on low, alternately add the dry ingredients in three additions, and the milk mixture in two, beginning and ending with the dry ingredients, and beating just until combined. Mix in the cooked and cooled apples.
Divide the batter evenly among the prepared pans. Bake for about 35 to 40 minutes, or until a cake tester inserted in the center of each cake comes out clean. Cool the cake in the pans on wire racks for about 20 minutes, then turn the cakes out onto the racks to complete cooling.