Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large bowl, cream the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add eggs and vanilla extract. Mix until fully incorporated.
In a separate bowl, whisk together flour, baking soda, cinnamon, and salt.
Gradually add dry ingredients to wet mixture and mix just until combined.
Gently fold in the peach pieces (tossed in flour to prevent sinking).
In a small bowl, prepare crumb topping: cut cold butter into flour, brown sugar, and cinnamon until mixture resembles coarse crumbs.
Scoop cookie dough onto prepared baking sheets. Sprinkle each cookie with a spoonful of crumb topping.
Bake for 12–14 minutes, or until edges are set and centers look slightly underbaked.
Cool on the baking sheet for 5 minutes before transferring to a wire rack.
Store in an airtight container for up to 1 week.