Preheat oven to 350 degrees. Line two 18 by 13-inch baking sheets with silicone baking mats or parchment paper.

In the bowl of an electric stand mixer fitted with the paddle attachment cream together butter granulated sugar and brown sugar until combined. Mix in egg, stop and scrape, then beat mix in the yolk and vanilla extract.

Add flour mixture and mix until combined, then mix in apples, and walnuts, if using.

Scoop dough out using a large cookie scoop, or 4 tablespoons at a time, and drop onto prepared baking sheets spacing cookies 2-inches apart.

Bake one sheet at a time in preheated oven until cookies are set, about 13 - 14 minutes.

Let cool on baking sheet several minutes then transfer to a wire rack to cool completely. Store cookies in an airtight container.

In a large bowl, beat the cream cheese until smooth. Then, add the powdered sugar, 1 Tablespoons of milk and vanilla. Beat just until combined. Do not over mix. Taste and add a pinch of salt and more vanilla if desired. Add a Tablespoon more of milk at a time until reach desired consistency. If you want it to drip down a dessert, you'll need a little more. If you want it thicker, use less or add a Tablespoon more of powdered sugar. Drizzle on the cooled cookies.