Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
In a mixing bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, ginger, and nutmeg. Set aside.
In a separate large bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the eggs one at a time, followed by the vanilla extract. Mix well.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Using a spoon or cookie scoop, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10 minutes or until the edges are lightly golden. The centers will look soft but will firm up as they cool.
Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a cooling rack.
To make the icing, mix the powdered sugar with milk until smooth. Drizzle over cooled cookies as desired.