Preheat oven to 350℉. Line an 11x 7 deep dish cookie sheet with Parchment paper
Add the butter to a medium saucepan set at medium heat. Allow the butter to brown until it smells toasted, about 3-5 minutes. You will see the butter change to an amber color. Remove from the heat and let it cool for about 5 minutes.
Once the butter is cooled, stir in the apple butter and 1 cup of brown sugar in the sauce pan. Let the mixture cool for another 5 minutes.
While the mixture is cooling, add the sifted flour, baking powder, cinnamon, nutmeg, and salt to a small bowl and set aside.
In a large bowl, whisk the eggs and vanilla. Add the butter mixture and combine well. Slowly add the flour and mix until well combined.
Spread the batter evenly on the baking sheet.
In a bowl, toss the apples with 1/2 cup of brown sugar and 1 tsp of cinnamon. Evenly spread the apples over the dough and pat them gently into it.
Transfer to the oven and bake for 20-30 minutes until the center is set. Let cool.