Preheat the oven to 360°F. Mix in a large bowl the flour and brown sugar.
Wash the peaches and cut them into 1cm slices. If you use organic fruit don't peel it to gain in flavor, fiber and vitamins.
Add to flour and sugar the plant milk, stirring with a wire whisk. The batter consistency should be assessed according to your flour, it could serve a little less or more milk than the specified to obtain a thick and soft (but not runny) batter.
Add the peaches to the cake batter and stir briefly.
Finally add sifted baking powder and stir well to distribute it evenly.
Cover with parchment paper (or brush lightly with oil) a 10" round baking pan or two 8" square baking pans.
Pour the batter into the prepared pan(s) and bake the cake(s) for 30 minutes.
After that try the cake(s) with the toothpick test and, if necessary, increase the cooking time by 5 to 10 minutes (you may need this if you bake the whole batter in a single pan).
When done let the cake cool completely on a wire rack before serving.