Preheat the oven to 350 degrees. Line a baking sheet with parchment paper.
Using an electric hand mixer, cream together the brown sugar and butter until light and fluffy. Add the egg and vanilla and mix until combined, making sure to scrape down the sides of the bowl.
In a separate bowl, combine the flour, oats, cinnamon, baking soda, cloves, salt, and nutmeg together until well combined.
Gradually add the oat mixture to the butter mixture until combined.
Sprinkle the lemon juice over the diced apples and toss to evenly coat them. Add the apples to the cookie dough and stir gently to combine.
Use a cookie scoop or spoon dough into rounds of about 2 tablespoons each, place a few inches apart on the prepared baking sheet.
Bake for 11-13 minutes, or until the tops are set and the edges are lightly golden.
Remove from the oven and cool on the baking sheet for a few minutes before transferring them to a wire rack to cool.
Make the maple glaze by combining the powdered sugar, maple syrup, and milk together until creamy and smooth.
Place the wire rack of cookies over a piece of parchment paper and drizzle the maple glaze over each cookie. Serve and enjoy.
Store cookies in an airtight container in the refrigerator for up to a week.