Melt the unsalted butter in a saucepan over medium heat, stirring frequently. Cook until it turns golden brown and releases a nutty aroma, then allow it to cool to lukewarm.

Finely grate the carrots using a box grater or food processor. Once grated, blot them with paper towels to remove excess moisture.

In a large mixing bowl, combine the cooled brown butter with light brown sugar and granulated sugar. Whisk until combined, then beat in the egg and vanilla extract until smooth.

In another bowl, whisk together flour, baking soda, cinnamon, nutmeg, and salt.

Gradually fold the dry ingredients into the wet mixture, mixing gently. Add in the blotted grated carrots and chopped pecans, if using.

Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.

Using a cookie scoop, form balls of dough and place them on the prepared baking sheets.

Bake in the preheated oven for 10-12 minutes, watching for the edges to turn golden brown. Let them cool on the trays for about 2 minutes.

In a mixing bowl, beat the cream cheese and granulated sugar until smooth. Gradually add milk to reach the desired consistency for icing.

Optional: Drizzle or pipe the cream cheese icing on cooled cookies.