Make the Cookies:
Preheat Oven: Preheat your oven to 350°F (175°C). Line two large cookie sheets with parchment paper or silicone baking mats. Set aside.
Mix Dry Ingredients: In a medium-sized bowl, whisk together the oats, flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
Combine Wet Ingredients: In a large bowl, whisk together the melted butter, pumpkin puree, granulated sugar, molasses, and vanilla extract. Add the eggs and whisk until smooth.
Form the Dough: Gradually fold in the dry oat mixture using a wooden spoon or silicone spatula, stirring until thoroughly combined.
Portion the Dough: Drop the dough by rounded tablespoons onto the prepared cookie sheets, spacing them about 2 inches apart. Use a medium-sized cookie scoop to make evenly sized cookies.
Bake: Bake the cookies in the preheated oven for 10 to 12 minutes, rotating the sheets halfway through, until the cookies are lightly browned. Let the cookies rest on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Make the Icing:
Prepare the Icing: In a medium bowl, whisk together the powdered sugar, cinnamon, water, and vanilla extract until smooth. If the icing is too thick, add a little more water, a teaspoon at a time, until you reach your desired consistency.
Ice the Cookies: Once the cookies have cooled completely, generously frost each one. Allow the glaze to harden completely before storing the cookies.