Preheat the oven to 180°C/160℃ fan/350°F/gas mark 4. Line a deep 20 cm (8 in) square cake tin with baking paper, making sure that you leave some overhanging on either side so that you can easily lift the cake out later.
To make the streusel topping, mix the flour, sugar and cinnamon together in a bowl. Add the butter and rub it in using your fingertips until no lumps of butter remain and the mixture is clumping together. Place in the fridge.
100 g (¾ cup + 1 Tablespoon) plain (all-purpose) flour, 50 g (¼ cup) light brown soft sugar, ½ teaspoon ground cinnamon, 70 g (5 Tablespoons) vegan block butter
Peel, core and cut the apples into approx 2 cm dice then toss them with the cinnamon, sugar and flour to coat. Set aside.
3 medium eating apples (about 350g), 1 Tablespoon light brown soft sugar, 1 teaspoon ground cinnamon, 1 Tablespoon plain (all-purpose) flour
To make the cake batter, whisk together the yogurt, milk, oil, vinegar, light brown sugar and vanilla extract in a large bowl until very well combined.
135 g (½ cup + 1 Tablespoon) vegan Greek style yogurt (I use Alpro), 120 g (½ cup) unsweetened non-dairy milk (I use soy), 82 g (90ml/6 Tablespoons) neutral oil (I use olive), 1 teaspoon vinegar, 150 g (¾ cup) light brown soft sugar, 1 Tablespoon vanilla extract
Whisk in the cornflour, baking powder and soda, cinnamon and salt then add the plain flour and gently stir with a balloon whisk until no dry lumps remain.
20 g (2 packed Tablespoons) cornflour (cornstarch), 1 ½ teaspoons baking powder, ½ teaspoon bicarbonate of soda (baking soda), 1 teaspoon ground cinnamon, ¼ teaspoon salt, 225 g (1 ¾ cups + 6 teaspoons) plain (all-purpose) flour
Spread a little more than half of the batter into the lined tin. Scatter over the apples in an even layer.
Dollop over the remaining batter and spread it out gently to cover the apples, it doesn't matter if they are poking through a bit. Scatter over the streusel evenly.
Bake for about 60 minutes until a skewer inserted into the centre comes out clean or with a few crumbs but no wet batter. Loosely cover the cake with tin foil after 45 minutes or so if the top starts to darken too much.
Leave the cake to cool in the tin for 20 minutes then use the overhanging baking paper to carefully lift it out of the tin onto a wire cooling rack. Leave to cool completely before slicing.