Preheat oven to 350 degrees F and grease an 11x17 inch sheet pan. You can also use a 9x13 inch pan but the cake will need to cook longer.
In a large bowl, add the flour, baking powder, salt and sugar and whisk well to combine.
Pour in the oil, milk, peach nectar or juice and vanilla. Mix with a large spoon until just combined, but be careful not to over mix.
Fold in the chopped peaches gently.
Pour into the prepared pan and bake for 25-30 minutes (or 40-50 minutes if using a 9x13 inch pan), or until a toothpick inserted comes out clean.
While the cake is baking, prepare the frosting: To a medium saucepan, add the vegan butter, milk and brown sugar. Bring to a boil and stir constantly until the butter has melted and the brown sugar dissolved. Remove from heat and whisk in the powdered sugar, gradually, until the frosting is smooth. Whisk in the vanilla as well.
Pour the warm frosting over the warm cake once it's done baking, spreading evenly with a spatula or spoon.
Let the cake and frosting cool for at least 30 minutes before serving, so the frosting can harden a bit. Cut into slices and enjoy!