Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
Finely chop the drained peaches and set aside.
In a medium bowl, whisk together flour, baking soda, cinnamon, and salt.
In a large bowl, mix melted butter, brown sugar, and white sugar until well blended.
Beat in the egg and vanilla extract.
Gradually stir in the dry ingredients until just combined.
Fold in the chopped peaches, white chocolate chips, and graham cracker crumbs.
Scoop dough onto the prepared baking sheets, spacing cookies 2 inches apart.
Bake for 12–14 minutes, or until edges are golden brown.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.