Preheat the oven to 180°C / 160°C fan / gas mark 4 and lightly grease a medium ovenproof dish.
In a large bowl, mix together the plain flour, cocoa powder, light brown sugar, baking powder, bicarbonate of soda, and salt.
Add the dairy-free milk, vegetable oil, and vanilla extract.
Stir until the mixture is smooth and fully combined.
Spoon the mixture into the prepared dish and level the top.
Bake for 28–30 minutes, or until the sponge is risen and a skewer inserted into the centre comes out clean.
Leave to stand for a few minutes before serving.
Serve warm on its own or with a suitable dairy-free custard or dairy-free cream alternative.