Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large mixing bowl, cream together the butter, brown sugar, and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, then stir in the molasses and vanilla extract.
In another bowl, whisk together the flour, baking soda, cinnamon, ginger, cloves, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Stir in the rolled oats until evenly distributed.
Drop dough by rounded tablespoonfuls onto the prepared baking sheet. Bake for 10-12 minutes, or until the edges are golden brown.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.
For the icing, whisk together the powdered sugar, milk, and vanilla extract until smooth. Drizzle over the cooled cookies.