01 - Place butter in a medium saucepan over medium heat. Cook, stirring continuously, until butter foams and develops golden-brown specks with a nutty aroma, about 4–6 minutes. Immediately transfer to a large mixing bowl and cool for 10 minutes.
02 - Add brown sugar and granulated sugar to the cooled brown butter. Whisk until thoroughly combined. Stir in eggs one at a time, followed by vanilla extract, mixing until smooth and glossy.
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 wet mixture and stir until just combined—do not overmix. Fold in oats, grated carrots, chopped nuts, 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. Cool on baking sheet for 5 minutes, then transfer to wire rack.
09 - Beat softened cream cheese and butter until smooth. Gradually incorporate powdered sugar and vanilla, mixing until creamy and lump-free. Drizzle over cooled cookies.