Preheat the oven to 350 degrees F or 175 degrees C. line cookie sheets with parchment paper or silpat.
In the bowl of your stand mixer (fitted with paddle attachment) or a deep mixing bowl, cream together butter, sugar and brown sugar till light and creamy, about 2-3 minutes.
Add egg and vanilla and mix until incorporated.
In a mixing bowl, add all purpose flour, baking soda, nutmeg, cinnamon and salt and whisk to combine.
Add the dry ingredients to wet and mix until just combined.
Stir in the grated carrots and sunflower seeds.
Drop dough by rounded tablespoonfuls onto cookie sheets. These cookie do not spread a lot.
Bake for 12-13 minutes, till the edges just start to brown. Removw fom oven, let cool on the cookie sheets for a few minutes and then transfer t a coling rack and let cool completely.