Preheat the oven: Preheat to 350°F (175°C). Grease an 8 × 8-inch (20 × 20 cm) baking dish with butter.
Prepare the apples: Place the peeled, cored, and chopped apples in the prepared dish. Add the granulated sugar, cinnamon, lemon juice, and vanilla extract. Toss to coat evenly, then spread into an even layer.
Mix the topping: In a bowl, combine the brown sugar, flour, oats, cinnamon, and salt. Add the cold, cubed butter and work it into the dry ingredients with a fork until the mixture is crumbly with small clumps.
Assemble: Sprinkle the oat topping evenly over the apples, covering the surface without pressing it down firmly.
Bake: Bake for 40–50 minutes, until the topping is golden, the juices are bubbling around the edges, and the apples are tender when pierced with a knife. If the topping browns too quickly, cover loosely with foil and continue baking.
Rest and serve: Remove from the oven and let rest for 15 minutes. Serve warm with vanilla ice cream, if desired.