Preheat oven to 350 degrees. Spray a 9x13 inch pan with cooking spray.
Whisk baking powder, salt, and flour in a medium bowl. Set aside.
Cream brown sugar and butter in the bowl of an electric mixer fitted with a paddle attachment. Add eggs and vanilla and beat until combined. Mix in dry ingredients. Stir in carrots.
Press into prepared pan (dough is sticky, spray your hands with cooking spray to avoid it sticking to your hands).
Bake at 350 for about 25-30 minutes. (Be careful not to overcook - the center will still be jiggly when you take these out of the oven and they will finish cooking and firming up as they cool. They stay super soft though!)
Cool completely in pan before frosting.
Make your frosting: Make sure your cream cheese is super soft. If it’s not, you can remove it from the package and heat it on HIGH in the microwave for about 10 seconds to soften it. You want it very soft but not melted.
Whisk cream cheese and butter together (you can also use a hand mixer). Whisk in powdered sugar. Add vanilla and cinnamon and whisk until smooth. Frost bars in pan.
You can eat these right after frosted and they’ll be gooey and good. Or, chill until the frosting sets and then slice and eat. Your preference!