Preheat the oven to 375°F.
Lightly grease an 8x8 or 9x9 baking dish.
Peel, core, and slice the apples.
Add the sliced apples to a large mixing bowl.
Add the brown sugar, flour, lemon juice, cinnamon, nutmeg, salt, and vanilla extract.
Stir until the apples are evenly coated.
Spread the apple filling into the prepared baking dish.
In a medium mixing bowl, stir together the flour, oats, brown sugar, cinnamon, and salt.
Add the butter and sourdough discard.
Mix until the topping comes together and looks crumbly.
Sprinkle the sourdough oat crumble topping evenly over the apple filling.
Bake at 375°F for 35 to 45 minutes, or until the filling bubbles around the edges and the topping is golden.
Let the apple crisp cool for 10 to 15 minutes before serving.
Serve warm with vanilla ice cream if desired.