Preheat the oven to 400°F (200 °C). Butter a large baking dish or casserole dish (10 inch (25 cm) diameter and fairly deep) and set it on a large rimmed baking sheet lined with parchment (to catch any drips). Set aside.
Oat crumble topping
In a large bowl, whisk together the all-purpose flour, oats, sugar, and salt. Add in the cubes of cold butter and toss it in the dry mixture to coat all the pieces. You can do this with your fingertips. Press and work the butter into the dry ingredients until you have a crumbly topping with lots of texture. Set aside. You can refrigerate the crumble topping if your kitchen is warm.
Apple filling
Peel and core the apples then slice them.
Wash, dry, and pick over the blueberries to remove any stems or twigs.
Toss the apples and blueberries with the cornstarch, sugar, lemon juice, and vanilla bean paste. Make sure the fruit is evenly coated. Pour the fruit evenly into the bottom of the buttered baking dish.
Scatter globs of the crumble topping over the fruit.
Bake the blueberry apple crumble for 40 minutes, then turn down the temperature to 350 ºF (175 °C). Continue baking until the fruit layer is bubbling, the topping is golden brown. This takes another 20 minutes or so.
Let cool on a wire rack. Serve warm or at room temperature with vanilla ice cream.
Notes
Feel free to modify the amount and type of thickener. You can try using more to achieve a thicker, more set fruit filling, and try arrowroot or tapioca starch instead of cornstarch.
I don't recommend using flour as a thickener because blueberries have too much water in them and the filling will be way too soupy, and also appear cloudy, if you use flour.