Preheat the oven to 180°C/160° fan/350°F/gas mark 4. Grease a 23 x 33 cm / 9 x 13 inch rectangular cake tin and line it with baking parchment.
Whisk together the milk, yogurt, oil, melted butter, sugar, vinegar and vanilla in a large bowl.
240 g (1 cup) unsweetened non-dairy milk (I use soy), 120 g (½ cup) plain non-dairy yogurt (I use soy), 83 g (6 Tablespoons) neutral oil (I use olive), 120 g (½ cup) vegan block butter, 250 g (1 + ¼ cups) caster or granulated sugar, 2 teaspoons vinegar, 1 Tablespoon vanilla extract
Use a balloon whisk to whisk in the baking powder, bicarbonate of soda and salt, followed by the flour. Be careful not to over-beat the batter, just mix it until no dry lumps remain.
2 teaspoons baking powder, ½ teaspoon bicarbonate of soda (baking soda), ½ teaspoon salt, 400 g (3 + ⅓ cups) plain (all-purpose) flour
Pour the batter into the prepared tin and spread it level. Bake for about 25 minutes until the cake is firm to the touch and a skewer inserted into the centre comes out clean.
Leave the cake to cool in the tin for 20 minutes then carefully turn it out onto a wire rack and leave to cool completely.
To make the icing, sift the icing sugar into a bowl, add the vanilla extract and gradually mix in enough water to make a very thick but pourable consistency. If it is too thick, add more water a couple of drops at a time, and if it is too runny add more sifted icing sugar.
450 g (4 cups) icing (powdered) sugar, 1 teaspoon vanilla extract, 4-5 Tablespoons water
Drizzle the icing over the cake (flip it upside down if you want a totally flat surface) and spread it level with a palette knife or the back of a spoon.
Scatter sprinkles generously over the icing while it is still wet, then leave it to set for about 30 minutes before slicing.
2-3 Tablespoons sprinkles