Preheat your oven to 350°F (175°C) and prepare your baking sheet with parchment paper.

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

Add the egg and vanilla extract to the creamed mixture and beat until well combined.

In a separate bowl, whisk together flour, baking soda, cinnamon, and salt, then gradually add to wet mixture, stirring gently.

Fold in the diced peaches, oats, and nuts if using, ensuring even distribution without breaking the fruit.

Drop rounded tablespoons of dough onto the prepared baking sheet, leaving space between each cookie.

Sprinkle cinnamon sugar over the top of each cookie before baking.

Bake for 10-12 minutes or until edges are golden and centers are slightly soft.

Cool on the baking sheet for a couple of minutes before transferring to a wire rack.