Preheat oven to 350 degrees F. Line two baking sheets with parchment paper, set aside.

To make the cookies, place the oats in a food processor and pulse for about 10 seconds to break them down. Don't pulse too much, as you want some texture in the oats themselves. In a large bowl, whisk together the oats, flour, baking powder, salt, cinnamon and nutmeg. Set aside.

Cream together the butter, brown sugar, and granulated sugar on high until light and fluffy. Stir in the egg and vanilla. Add in the dry ingredients and stir until evenly combined. Using a small ice cream scoop, portion out out the dough onto the prepared baking sheets, making sure to leave about 2 to 3 inches of space in between the cookies to allow room for spreading. Bake until lightly golden brown around the edges, about 10 to 12 minutes. Remove from the oven and let cool on the baking sheets for about 10 minutes. Transfer to a wire rack and let cool completely.

To make the icing, in a large bowl, whisk together the powdered sugar, heavy cream, water, and vanilla extract until smooth. Gently and very lightly dip the top of the cooled cookies into the icing, and return to the wire rack to set.

Once the icing has set, flip over half of the cookies and place a scoop of ice cream onto each. Then sandwich together with the remaining cookies. Place on a baking sheet and freeze until firm, about 3 to 4 hours or overnight before serving. Leftovers can be wrapped in plastic wrap individually and stored in the freezer for up to 2 weeks. Enjoy!