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 plain flour, light brown soft sugar, caster sugar, baking powder, bicarbonate of soda, pumpkin spice and salt in a large mixing bowl.
Add the pumpkin puree, sunflower oil, non-dairy milk, vinegar and vanilla extract and whisk gently until no dry lumps remain but be careful not to over-mix.
Transfer the batter to the prepared tin and spread it level. Bake for about 25 minutes until a skewer inserted into the centre comes out clean or with a few moist crumbs but no wet batter.
Leave the cake to cool in the tin for 15 minutes then carefully lift it out onto a wire rack and leave it to cool completely before icing it.
To make the coffee buttercream, place the softened vegan block butter and instant espresso powder in a bowl and whisk until smooth.
Add the sifted icing sugar and vanilla extract and whisk on a high speed for a good few minutes until the buttercream is very light and fluffy and the espresso powder has dissolved.
If it is too thick you can whisk in a little non-dairy milk, ½ teaspoon at a time. And if it is too soft you can either whisk in more sifted icing sugar or pop it in the fridge for 15 minutes to firm up a bit.
Spread the buttercream over the cake, decorate as you like and serve.