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Preheat oven to 350F and line 2 cookie sheets with parchment paper.
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Stir together the oats, flour, baking powder, baking soda, cinnamon, nutmeg and salt. Set aside.
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In the bowl of a stand mixer fitted with a paddle attachment, beat together the melted butter, sugar and brown sugar until light and fluffy.. Add eggs, one at a time, mixing until combined. Mix in the dry oat mixture. mixing until just combined.
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Drop dough by (heaping) rounded tablespoons onto prepared cookie sheets and flatten slightly with the bottom of a glass or something similar. Bake for 14-16 minutes, rotating halfway through, until browned. Let cookies cool on the baking sheets for 5 minutes before moving to a wire rack to cool completely.
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To make the glaze, whisk together the powdered sugar and milk until no lumps remain. Glaze each cookie and allow to harden before serving.