01 - Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
02 - In a medium bowl, whisk together rolled oats, all-purpose flour, ground cinnamon, ground nutmeg, baking soda, and salt until thoroughly blended. Set mixture aside.
03 - In a large bowl, beat softened butter, light brown sugar, and granulated sugar with an electric mixer until the mixture appears light and fluffy, approximately 2 minutes.
04 - Add the large egg and vanilla extract to the creamed butter mixture. Continue mixing until completely incorporated and smooth.
05 - Gradually add the prepared dry ingredient mixture to the wet ingredients. Mix on low speed just until flour streaks disappear, being careful not to overmix.
06 - Gently fold the diced peaches and raisins into the cookie dough using a spatula, distributing them evenly throughout the batter.
07 - Using a cookie scoop or tablespoon, drop rounded spoonfuls of dough onto the prepared baking sheets, leaving approximately 2 inches of space between each cookie to allow for spreading.
08 - Sprinkle coarse sugar generously over the tops of the cookie dough mounds if desired for extra texture and sweetness.
09 - Bake for 12 to 14 minutes until the edges turn golden brown and the centers appear set. The cookies should still look slightly soft in the middle.
10 - Allow cookies to rest on the baking sheet for 5 minutes to firm up before transferring to a wire cooling rack to cool completely.