Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a large bowl, cream the softened butter with brown sugar and granulated sugar until fluffy.
Beat in the egg and vanilla until smooth.
Add the dry ingredients to the wet ingredients and mix just until you don’t see dry flour.
Fold in the grated carrots (and oats/nuts/raisins if using). The dough should look thick and scoopable.
Scoop dough into rounded tablespoons (or use a cookie scoop) and place a few inches apart on the baking sheets.
Bake 10–12 minutes, until the edges look set and lightly golden but the centers still look soft.
Let cookies cool on the sheet for 5 minutes, then transfer to a rack to cool completely.
For the glaze, beat cream cheese until smooth, then mix in powdered sugar and vanilla. Add a tiny splash of milk or lemon juice until it becomes drizzle-thick.
Drizzle or spread over cooled cookies and let set before serving.