Preheat oven to 350 degrees.Grease a 11x7 baking pan. I lined with parchment paper and sprayed with non-stick cooking spray as well. That makes it easier for me to pull the bars out to cut.
In a large bowl, add oil, granulated and brown sugar, peanut butter, eggs, and vanilla. Mix with a hand mixer on medium until well combined.
In a separate bowl, add in flour, cinnamon, salt, baking soda, and baking powder. Stir together with a spatula.
Combined the dry ingredients with the wet ingredients. Mix with a hand mixer on low until the dry ingredients are incorporated.
Add in the zucchini and carrots and stir until thoroughly incorporated.
Pour out onto a prepared pan. Spread out evenly with a spatula.
Place in the oven and bake for 45 - 47 minutes or until done. Place a toothpick into the center of the squares, if it comes out with moist crumbs it's done. If batter comes out, let it bake longer.
Let cool and frost.
Frosting
In a large bowl, combine butter and cream cheese. Beat with the hand mixer until the mixture is smooth and well combined.
Add in vanilla and powdered sugar. Mix on low until the powdered sugar is well incorporated. Turn mixer on high and mix for an additional minute or two.