Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the eggs one at a time, then add the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, salt, and cinnamon.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Gently fold in the diced peaches and white chocolate chips (if using).
Using a cookie scoop or spoon, drop dough onto the prepared baking sheets, spacing them about 2 inches apart. Sprinkle the tops with a little granulated sugar.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers will still look a bit soft but will set as they cool.
While the cookies are baking, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the consistency by adding more milk if necessary.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack. Once completely cooled, drizzle the glaze over the cookies.
