Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
Whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg in a medium bowl. Set aside.
Beat butter with both sugars on medium speed for 2 to 3 minutes until fluffy and pale.
Add eggs one at a time, mixing after each. Mix in the vanilla extract.
Fold in the dry ingredients with a spatula until just combined. Do not overmix.
Scoop dough into 2-tablespoon balls and place 2 inches apart on prepared baking sheets.
Bake for 10 to 12 minutes until edges are set and centers look slightly underdone.
Cool on the pan for 5 minutes, then transfer to a wire rack.
Mix powdered sugar, milk, and cinnamon to make the glaze, then drizzle or spread over cooled cookies.