01 - Place butter in a medium saucepan over medium heat. Cook, stirring constantly, until butter foams and develops golden-brown specks with a nutty aroma, about 4–6 minutes. Immediately pour into a large mixing bowl and cool for 10 minutes.
02 - Whisk brown sugar and granulated sugar into the cooled brown butter until smooth. Beat in eggs one at a time, followed by vanilla extract, mixing until fully incorporated.
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 and stir until just combined—do not overmix. Fold in oats, grated carrots, walnuts or pecans, and raisins if using.
05 - Cover bowl and refrigerate for 30 minutes to enhance chewiness and prevent excessive spreading during baking.
06 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
07 - Scoop dough into 2-tablespoon balls, placing them 2 inches apart on prepared baking sheets.
08 - Bake for 11–13 minutes, until edges are set but centers appear slightly underbaked. Let cookies cool on baking sheet for 5 minutes before transferring to a wire rack.
09 - Beat softened cream cheese and butter until smooth. Gradually incorporate powdered sugar and vanilla, beating until no lumps remain. Drizzle over completely cooled cookies.