Preheat oven to 350°F. Line two large baking sheets with parchment paper. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and cloves. Set aside.
In a large mixing bowl, cream 1 cup softened butter with brown sugar and granulated sugar until light and fluffy, about 3 minutes with an electric mixer.
Beat in pumpkin puree, eggs, and 2 teaspoons vanilla until fully incorporated. The mixture will look slightly loose.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Fold in 3 cups rolled oats with a spatula.
Scoop rounded tablespoons of dough onto prepared baking sheets, spacing them 2 inches apart. Bake for 12-14 minutes until edges are lightly golden but centers still look soft.
Let cookies cool on baking sheet for 5 minutes, then transfer to a wire rack. Cool completely before icing.
For the icing, beat 8 oz cream cheese and 1/2 cup softened butter until smooth. Add powdered sugar, 2 teaspoons vanilla, 1 teaspoon cinnamon, and 3-4 tablespoons cream. Beat until fluffy.
Dip or spread icing onto cooled cookies. Let set for 15 minutes before serving.