Preheat the oven to 350 °.
Coat the interior of an 8-inch pan, bottom and sides, with a teaspoon of unsalted butter. It is important to cover the entire pan with butter.
It helps if the peaches are very ripe. Peel both peaches and cut them into ¼-inch slices.
Sprinkle 2 tablespoons of light brown sugar on the bottom of the pan.
Fan the peach slices on the bottom of the pan, around the sides. Once the first layer is completed, fan more peaches in the middle of the pan. The entire bottom of the pan should be covered with peaches.
Sprinkle 2 tablespoons of light brown sugar on top of the peaches.
Add dry ingredients - flour, cornmeal, baking powder, salt - to a medium bowl. Mix with a whisk to ensure all ingredients are combined.
In another medium bowl, combine 2 eggs with the granulated sugar. Slowly stream the olive oil into the batter while combing with a whisk. Add the milk and the vanilla extract.
Add the dry ingredients to the wet, using a whisk to incorporate. As soon as everything is combined, stop whisking. The batter will be thick.
Slowly pour the batter into the prepared pan over the peaches. Be careful so the peaches are not disturbed.
Place the pan in the oven. Bake the cake for 50 minutes.
At the 45-minute mark, insert a toothpick into the cake. If the toothpick still has crumbs stuck to it, return the cake to the oven. Bake for 5 more minutes.
If the toothpick is clean, take the cake out of the oven. The top of the cake should feel firm in the center.
Let the cake cool for 15-20 minutes. Run a knife around the inside of the pan, releasing the cake. Place a plate on the top of the pan. While holding the plate and the pan, flip the cake over. The plate should be on the bottom. Slowly pull the pan off the cake.