Preheat the oven to 350°F and line two baking sheets with parchment paper.
Whisk the dry ingredients: combine rolled oats, flour, baking soda, salt, cinnamon, ginger, nutmeg, and cloves in a medium bowl.
Cream the butter and sugars until smooth and fluffy. Beat in the egg yolk, molasses, vanilla, and blotted pumpkin puree.
Mix in the dry ingredients just until combined. Chill the dough for 20 minutes if it is sticky.
Scoop and shape 1 1/2 tablespoon portions of dough onto baking sheets, leaving space between cookies. Gently flatten each portion.
Bake for 11 to 13 minutes, until edges are set and centers remain soft. Cool on the baking sheet for 10 minutes, then transfer to a wire rack.
Make the icing by beating cream cheese, butter, powdered sugar, cinnamon, and milk until smooth and drizzle-friendly.
Ice cooled cookies with the spiced cream cheese icing, then allow the topping to set before serving.