Preheat oven to 350 degrees F. Grease and flour the pan and line the bottom with parchment.
Whisk the cake flour, baking powder, baking soda, and salt in a medium bowl. Set aside.
In a stand mixer, beat the butter, oil, and sugar on medium speed for 3 minutes until light and fluffy.
Add eggs one at a time, mixing until just combined after each.
Mix in the sour cream, vanilla, and cinnamon until smooth.
With the mixer on low, add the flour mixture in three additions, mixing just until combined.
Toss the diced peaches in a spoonful of reserved flour, then gently fold into the batter.
Pour into the prepared pan, top with extra sliced peaches, and bake for 45 to 55 minutes, until a toothpick comes out clean.
Cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.
If using, beat the cream cheese and butter until smooth, add powdered sugar gradually, then mix in vanilla and salt until fluffy.
Once the cake is completely cool, spread the frosting evenly over the top with an offset spatula, then slice and serve.