Preheat oven to 350 degrees. Spray a large jelly roll pan (12x18x1-inch) with non-stick cooking spray.
In a large mixing bowl, combine eggs, oil, brown butter, sugar, and pumpkin and stir until combined. In a separate medium bowl, whisk together flour, baking powder and soda, salt, cinnamon, ginger, cloves, and nutmeg until combined. Add the dry ingredients to the wet, and stir until combined. Pour into prepared baking sheet. Bake for 25-30 minutes and toothpick comes out clean. Cool completely before frosting.
Beat cream cheese, brown butter, vanilla, and milk together until smooth. Add in powdered sugar, 1 cup at a time until desired consistency is reached. Spread evenly over cooled bars. Slice and serve!
These bars freeze very well, just store in an air tight container.
See the blog post for the "How to Make Brown Butter" link. You can make it in advance so that it becomes a solid butter again. You don't want to use melted butter in the frosting or the frosting consistency will be too runny.