Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.

In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy (about 3-4 minutes).

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.

Gradually add the dry ingredients to the wet mixture, alternating with the milk, starting and ending with the flour mixture. Mix until just combined.

Gently fold in the diced peaches until evenly distributed throughout the batter.

Pour the batter into the prepared cake pan and smooth the top with a spatula.

Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.