Preheat oven to 350° F. Line an 8x8-inch baking pan with parchment, leaving about an inch overhang on either side.
In a large bowl, combine the flour, cheese, sugar, salt, melted butter and egg and stir together until a dough is formed.
Press the dough evenly into the bottom of the baking pan with your hands, pressing it all the way to the edges and in the corners. Bake for about 20-25 minutes, until golden brown.
To make the crumble, combine the flour, brown sugar, salt, vanilla and butter in a medium bowl. Toss the butter to coat in the flour then gently squeeze the butter into the flour mixture to form fists. Repeat until large clumps form. Crumble up the large chunks to form smaller pea-sized crumbles. Place mixture in fridge while you assemble the filling.
In a large bowl, add in the apples, apple cider vinegar, flour, sugar, cinnamon and salt and toss to combine. Pour filling evenly over slightly cooled crust and sprinkle top with crumb topping.
Bake for about 25-30 minutes or until filling is bubbling and crumble topping is golden brown. Allow to cool completely before slicing into 12 square bars.