In a medium bowl, whisk together the all-purpose flour, old-fashioned rolled oats, ground cinnamon, baking soda, ground nutmeg, and kosher salt. Mix until well combined and set aside.
In a stand mixer fitted with a paddle attachment, add the unsalted butter and both the brown sugar and granulated sugar. Beat together on medium speed until light and fluffy, about 2 minutes.
Add in the large egg and vanilla extract to the butter-sugar mixture. Beat until fully incorporated.
Carefully pour the dry ingredients into the wet ingredients and mix on low speed just until combined.
Gently fold in the finely diced apple until evenly distributed throughout the dough.
Prepare two baking sheets by lining them with parchment paper. Use a 2-tablespoon-sized cookie scoop to drop rounded balls of cookie dough onto the prepared sheets.
Once all the dough is scooped, place the baking sheets in the freezer for 10 minutes.
While the cookie dough chills, preheat your oven to 350°F (175°C).
After the dough has chilled, take the baking sheets out of the freezer and place them in the oven. Bake for 10 to 12 minutes.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
Once cooled, enjoy your delicious Apple Cinnamon Breakfast Cookies or store them in an airtight container for later!