Cut apples into thin slices using a mandoline or a sharp knife. Place apples, brown sugar, butter, lemon juice, vanilla, cinnamon, and nutmeg in a large bowl; toss to coat. Divide apple mixture evenly among 4 (6-ounce) ramekins, arranging apple slices in a fan shape. Sprinkle each ramekin evenly with crumbled oatmeal cookies. Bake at 425° for 9 minutes or until the apples are crisp-tender.