Preheat the oven to 350°F (175°C).Toss the sliced apples with both sugars, lemon juice, vanilla, cinnamon, nutmeg, and flour.Spread the apple mixture evenly into a greased baking dish.In another bowl, combine oats, flour, brown sugar, cinnamon, and salt.Cut the cold butter into the mixture until coarse crumbs form.Sprinkle the crumble evenly over the apples.Bake for 40–45 minutes, until the topping is golden and the apples are tender.Let cool for 15 minutes before serving.Serve warm with vanilla ice cream or whipped cream.