Preheat oven to 180 C / Gas 4. Lightly grease a 20cm square baking tin.
Mix sugar, flour, cocoa powder, baking powder and salt together in a large bowl. Push mixture to the sides of the bowl to form a well in the centre.
Combine yoghurt, coffee, apple sauce and vanilla extract in a small bowl. Pour yoghurt mixture into the flour mixture. Fold gently with a spatula until just combined. Spread in the prepared tin.
Bake in the preheated oven until centre is firm to the touch, 45 to 55 minutes. Cool slightly before cutting into squares, about 15 minutes.