Preheat oven to 350°F.
Rinse and cut apples in half, lengthwise. Remove any stems. Cut out center core of apple that contains the seeds. Do not peel.
Place apples cut side down. Use a sharp knife to cut apples into 1/8 - inch slices.
In a large bowl, combine sliced apples, ¼ cup of brown sugar, 1 Tablespoon of flour, cinnamon, and nutmeg, if using. Mix well.
Spray baking dish with non-stick cooking spray.
Pour apple mixture into baking dish. Spread evenly.
Dice butter into smaller cubes, using a sharp knife. In a medium bowl, combine remaining brown sugar and flour, oats, and butter. Mix with hands until crumbly.
Spread oat and flour mixture over apple mixture. Bake uncovered on middle rack of oven for 40 minutes or until top is lightly browned or bubbly.
Let sit for 15 - 20 minutes before serving.