01 - Place butter in a medium saucepan over medium heat. Cook, stirring constantly, until butter foams, turns golden brown, and develops a nutty aroma, approximately 4–6 minutes. Immediately pour into a large mixing bowl and let cool for 10 minutes.
02 - Add brown sugar and granulated sugar to the cooled brown butter. Whisk vigorously until thoroughly combined. Stir in eggs one at a time, followed by vanilla extract, mixing until smooth and creamy.
03 - In a separate bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger until evenly distributed.
04 - Add dry ingredients to the wet mixture. Stir gently until just combined—do not overmix. The dough will be thick and slightly sticky.
05 - Gently fold in oats, grated carrots, walnuts or pecans, and raisins if using, until evenly distributed throughout the dough.
06 - Cover bowl and refrigerate dough for 30 minutes to enhance chewiness and prevent excessive spreading during baking.
07 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
08 - Scoop dough into 2-tablespoon balls, placing them 2 inches apart on prepared baking sheets.
09 - Bake for 11–13 minutes, until edges are set but centers appear slightly underbaked. Let cool on baking sheet for 5 minutes before transferring to wire rack to cool completely.
10 - Beat softened cream cheese and butter until smooth. Add powdered sugar and vanilla, continuing to beat until creamy and well combined. Drizzle over completely cooled cookies.