Line the bottom of a cake pan with parchment paper.
Pour 2 tablespoons of melted vegan butter and swirl it around so it coats the bottom of the pan.
Sprinkle ¼ cup of sugar evenly over the butter. Arrange the peaches over the butter and sugar in a decorative pattern.
In a bowl, beat the remaining 6 tablespoons butter with 1 cup sugar using a handheld electric beater until fluffy, about a minute. You can also do this in the stand mixer.
Add non-dairy milk, pure vanilla extract and apple cider vinegar. Mix them in.
Add the flour, baking soda, baking powder, cinnamon and salt to the bowl.
Beat for a few seconds with the electric beater to mix. Scrape down the sides and the bottom of the bowl halfway through beating to ensure there's no dry flour in the bowl.
Pour the batter over the peaches in the cake pan. Smooth the top with a spatula. Bake in a 350-degree Fahrenheit/180-degree Celsius oven for 30-35 minutes or until a toothpick in the center comes out clean.
Cool the cake on a rack for 10 minutes, then place a plate over the cake pan and quickly invert it to release the cake. Peel off the parchment paper carefully. If any peach slices stick to the parchment just rearrange them back on the cake.
Dust the cake with powdered sugar before serving (optional).