Preheat oven to 350 degrees. Line a 9x13 baking dish with parchment. Place the prepared pan in the freezer.
Stir together the flour, baking soda, salt, cinnamon, and nutmeg. Stir in the oats and sugar. In a separate bowl, mix together the melted butter, sugar, eggs, and vanilla. Combine the wet ingredients with the dry and mix until well combined.
Press half of the dough into the prepared pan. Set aside.
Roll the remaining dough between two pieces of parchment paper into a 9x13 rectangle. Place in the freezer on a cookie sheet.
Peel, quarter, and thinly slice the apples. Arrange them over the dough in rows so that each slice slightly overlaps another.
Remove the rolled dough from the freezer and peel off one layer of parchment. Place the dough on top of the apples and remove the other piece of parchment. Press the dough in to cover the apples.
Bake for 25 to 30 minutes or until lightly browned and cooked through. Cool in the pan and then cut into squares to serve.