For the sorbet, place the sugar, water, lemon juice and liquid glucose into a pan over a low heat.
Stir the mixture and slowly bring to the boil. Boil the mixture for five minutes, then remove from the heat and allow to cool. Place into the fridge to chill.
Meanwhile, for the blackberries, place the blackberries, sugar and water into a clean pan over a low heat. Cook gently to soften the fruit.
Pass the blackberry mixture through a sieve into a bowl.
Add the blackberry mixture to the chilled syrup and churn in an ice cream maker according to manufacturer's instructions.
Transfer to a freezer-proof container and freeze until needed.
For the tart, preheat the oven to 180C/365F/Gas 4.
Cut out the pastry into four equal squares of approx 15cm/6in and place onto a baking tray.
Lay the apples in straight lines across each piece of pastry, overlapping each other, to cover each piece of pastry.
Sprinkle with sugar, then place into the oven to bake for 12-15 minutes, or until golden-brown and cooked through.
To serve, transfer each apple tart to a plate while still warm and place a scoop of blackberry sorbet on top. Garnish with a mint sprig.