Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large mixing bowl, cream together softened butter, brown sugar, and granulated sugar until light and fluffy.
Add eggs and vanilla extract. Beat until fully incorporated.
In a separate bowl, whisk together flour, baking soda, salt, and cinnamon.
Gradually add dry ingredients to the wet mixture and mix until a dough forms.
Gently fold in diced peaches using a spatula.
Scoop dough into 2-tablespoon portions and place 2 inches apart on prepared baking sheets.
Bake for 11–13 minutes or until edges are golden brown. Centers should look slightly underbaked.
Cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
For the glaze, whisk together powdered sugar, peach puree, and vanilla extract until smooth.
Drizzle cooled cookies with peach glaze. Allow glaze to set before serving.