Preheat oven to 350ºF. In a large bowl, combine flour, baking soda, salt and cinnamon. Stir together and set aside.

Using a sharp knife, remove the skin from peaches and cut into small chunks. Place the diced peaches on a paper towel and set aside.

In a large bowl, cream together butter and sugars until light and fluffy, about 3 minutes. Add egg and vanilla, beat until combined. Add flour mixture and beat on low speed until well incorporated. Gently fold in the diced peaches.

Using a cookie scoop or tablespoon, drop in rounded spoonfuls on cookie sheets, leaving plenty of room between cookies to allow for some spreading. Bake for about 10-12 minutes, or until light golden brown. Cool about 1 minute on cookie sheets and then transfer to wire racks to cool completely.

If using glaze: Mix together the powdered sugar, cream and vanilla until smooth. Drizzle lightly over the cookies while still warm, allow to cool. Serve with a cold glass of milk and enjoy.