01 - Place butter in medium saucepan over medium heat. Cook, stirring constantly, until butter foams and develops golden-brown specks with nutty aroma, about 4-6 minutes. Immediately transfer to large mixing bowl and cool for 10 minutes.
02 - Whisk brown sugar and granulated sugar into cooled brown butter until fully combined. Add eggs one at time, followed by vanilla extract, mixing until smooth and glossy.
03 - In separate bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger until evenly distributed.
04 - Add dry ingredients to wet mixture, stirring until just combined with no visible flour streaks. Do not overmix.
05 - Gently fold in oats, grated carrots, walnuts or pecans, and raisins until evenly distributed throughout dough.
06 - Cover bowl and refrigerate for 30 minutes to enhance chewiness and prevent excessive spreading.
07 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
08 - Scoop dough into 2-tablespoon balls, placing 2 inches apart on prepared baking sheets.
09 - Bake for 11-13 minutes until edges are set but centers appear slightly underbaked. Cool on baking sheet for 5 minutes before transferring to wire rack.
10 - Beat softened cream cheese and butter until smooth. Add powdered sugar and vanilla, mixing until creamy. Drizzle over completely cooled cookies.