Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat for easy cleanup.
Prepare the Peaches:
If using fresh peaches, peel and chop them into small cubes. If using canned peaches, drain them well and chop them into small pieces. Set aside.
Make the Dough:
In a large mixing bowl, cream together the softened butter and granulated sugar using a hand mixer or stand mixer until light and fluffy (about 2-3 minutes).
Add the egg and vanilla extract to the butter mixture, mixing until fully incorporated.
Add the Dry Ingredients:
In a separate bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg (if using).
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the Peaches and Optional Add-ins:
Gently fold the diced peaches into the cookie dough, being careful not to break them up too much.
If you’re adding oats and nuts, fold those in as well. The dough will be slightly thick but should hold together.
Scoop the Dough:
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Gently flatten each cookie with the back of a spoon or your fingers to help them spread evenly as they bake.
Sprinkle with Brown Sugar:
Sprinkle a small amount of brown sugar over the top of each cookie before baking for a nice, caramelized finish.
Bake the Cookies:
Bake for 10-12 minutes, or until the edges are golden brown and the centers are set. The cookies may look slightly soft in the center, but they will firm up as they cool.
Cool and Serve:
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.