Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat. Dice the fresh peaches into small, even pieces, set aside.
In a large mixing bowl, use an electric mixer to cream together the softened butter, brown sugar, and granulated sugar until the mixture is light and fluffy, about 3 to 4 minutes.
Beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and ground cinnamon.
Gradually add the dry ingredients to the wet mixture, mixing just until combined. Then gently fold in the diced peaches, oats, and chopped nuts.
In a small bowl, combine the brown sugar, flour, melted butter, and ground cinnamon for the topping. Mix until crumbly and coarse.
Scoop cookie dough onto the prepared baking sheet, spacing about 2 inches apart. Use about 2 tablespoons of dough per cookie. Generously sprinkle the crumble topping over each portion, pressing lightly so it adheres.
Bake for 12-15 minutes, or until edges are golden and topping is crisp. Let cool on baking sheet 5 minutes before transferring to a wire rack to cool completely.