Whiz the butter, flour and 1/2 cup (110g) caster sugar in a food processor until the mixture resembles fine breadcrumbs. Add the egg and vanilla, then blitz to combine. Shape into a ball, then enclose in plastic wrap and chill for 20 minutes.
Meanwhile, place the apple, blueberries, lime juice, remaining 1/4 cup (55g) caster sugar and 1/2 cup (125ml) water in a large pan. Bring to a boil, then reduce the heat to medium and simmer for 15-20 minutes until the apples are soft and most of the liquid has evaporated. Remove from heat, cool, then blend until smooth. Set aside.
Preheat oven to 180°C. Grease and line a 24cm x 30cm cake pan with baking paper. For the crumble, whiz flour and butter in a food processor until mixture resembles breadcrumbs. Add remaining ingredients and pulse to combine.
Remove the biscuit pastry from the fridge, then unwrap and flatten into a disc. Place between 2 pieces of baking paper and roll out into a 24cm x 30cm rectangle, then use to line the cake pan.
Prick the base all over with a fork, then bake for 20 minutes or until starting to brown. Cool for 5 minutes, then spread jam over base. Scatter over crumble, then sprinkle with remaining 2 tbs brown sugar.
Bake for a further 25-30 minutes or until golden. Allow to cool for 30 minutes or until firm, then cut into squares and serve.