Combine apple, blackberries, caster sugar, lemon juice, cornflour, cinnamon and vanilla in a slow cooker. Cover and cook, gently stirring once, for 2 hours on high (or 3 hours on low) or until the apple is tender and sauce thickens slightly.
Meanwhile, combine the flour, brown sugar and extra cinnamon in a bowl. Add the butter. Use your fingertips to rub butter into the flour mixture until the mixture resembles fine breadcrumbs. Make a well in the centre. Add the egg yolk and buttermilk. Use a round-bladed knife to stir until a soft dough forms.
Drop tablespoonfuls of buttermilk mixture over the apple mixture in the slow cooker. Sprinkle with the walnut and demerara sugar. Cover and cook for 1 hour on high (or 1 1/2 hours on low) or until the topping is golden.
Divide the cobbler among serving bowls. Serve with ice cream.