Preheat oven to 350°F (175°C or 180°C). Line baking sheets with parchment paper or silicone baking mats.

In a medium bowl, whisk together the flour, oats, cinnamon, baking soda, and salt. If using, also whisk in allspice and nutmeg. Set aside.

In a large mixer bowl, cream together the room temperature butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 3-5 minutes. Scrape down the sides of the bowl as needed.

Add the egg and vanilla extract. Beat for 1-2 minutes or until well combined, scraping the sides of the bowl with a spatula.

Toss the finely chopped apples with lemon juice to prevent browning.

Add the dry ingredients to the wet mixture and mix on low speed until just combined. Do not overmix.

Gently fold in the lemon-coated apples. If using, also fold in chopped white chocolate and walnuts. The dough will be thick and sticky.

Scoop the dough with a 2-3 tablespoon ice cream scoop (about 35-40g or 1.4oz per ball) and roll the dough into balls between your hands. Place them on the prepared baking sheets about 2 inches (5 cm) apart. Press down gently to slightly flatten the tops, but do not squish them flat.

Bake for 12-15 minutes, or until the edges are lightly golden and the centers are set but still look soft. The cookies will be a little puffy when you take them out of the oven and will settle as they cool.

Remove cookies from the oven and allow to cool on the baking sheets for 5-10 minutes before transferring to a wire rack to cool completely.

If making the maple glaze: In a small bowl, combine powdered sugar, milk, and maple syrup. Whisk until smooth. Adjust consistency with additional milk or powdered sugar if necessary.

Drizzle the maple glaze over each cooled cookie. Let the glaze set before stacking or storing.