Preheat your oven to 340°F (170°C).
Melt the butter and pour it into the bottom of a lined 8-inch cake pan. Sprinkle the brown sugar over the butter, then arrange the peach slices on top. Set aside.
Mix the dairy-free milk with the apple cider vinegar and let it sit for a few minutes to thicken.
Add the remaining wet ingredients to the milk mixture.
Sift in the dry ingredients and gently mix until combined.
Pour the batter into the prepared pan, covering the peaches. Bake for 40 to 50 minutes, or until the cake is risen and fully cooked.
Once baked, flip the cake onto a serving plate and let it cool before slicing and serving.