Preheat your oven to 350°F (175°C). Prepare a greased 9-inch baking dish.

Peel and slice the ripe peaches and set them aside.

In a large mixing bowl, cream together the softened unsalted butter and sugar until light and fluffy.

Add the egg and vanilla extract, mixing until combined.

In another bowl, whisk together the all-purpose flour, baking powder, cinnamon, and salt. Gradually add this dry mixture to the wet mixture, stirring until just combined.

Gently fold in the oats.

Pour half of the batter into the prepared baking dish.

Layer the sliced peaches on top.

Add the remaining batter on top of the peaches.

In a small bowl, combine brown sugar and oats with a little melted butter and sprinkle this crumb mixture over the cake.

Bake in the preheated oven for 35-40 minutes, or until the cake is golden brown and a toothpick inserted into the center comes out clean.

Allow the cake to cool slightly before slicing. It can be served warm or at room temperature.