Preheat the oven to 350°F (175°C). Grease and flour the 9-inch round cake pan.
In a mixing bowl, combine the flour, baking powder, baking soda, salt, and ground cinnamon. Set aside.
In a separate large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
Gradually add the dry flour mixture to the butter mixture, alternating with the buttermilk, starting and ending with the flour mixture. Mix until just combined.
Gently fold in the diced peaches until evenly distributed in the batter.
Pour the batter into the prepared cake pan and spread it evenly.
In a small bowl, mix the brown sugar, rolled oats, and remaining cinnamon. Sprinkle this crumb mixture evenly over the top of the cake batter.
Bake in the preheated oven for about 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.