Make the Brown Butter: In a nonstick pan over medium heat, melt the butter. Continue cooking the butter – stirring constantly. The butter will get foamy, then bubbly, then start to turn turn golden brown and develop a nutty/caramely aroma. Once it reaches a deep golden color, remove from the heat and pour into a bowl to chill in the fridge or freezer until it's room temperature. It doesn't have to come back to solid before using. See note below if you do bring it back to a solid/softened state.

Prep: Preheat your oven to 350℉. Spray a 9x13 pan with nonstick spray and line with parchment paper.

Make the Bars: In a large mixing bowl, whisk together the eggs, sugar, oil, pumpkin, and maple syrup. Stir in the dry ingredients until just combined (check for any dry bits hiding in the bottom of the bowl) - a few lumps in the batter is fine. Do not over mix!

Bake: Pour batter into your prepared pan. Bake for 25-29 minutes, or until a toothpick inserted into the center of the cake comes out with moist crumbs, not wet batter. Let the cake cool in the pan for 10 minutes, then invert it onto a cooling rack to cool completely. (Letting it cool upside down on the rack keeps the flatter for easy frosting!)

Make the Frosting: Cream together your room temperature brown butter and cream cheese in a large mixing bowl on high for 1-2 minutes. Add half the powdered sugar and mix until just incorporated. Add the remaining powdered sugar, milk, cinnamon, vanilla, and a pinch of salt and mix until creamy.

Serve + Store: Frost the cake when cool. Dollop pumpkin butter over the frosting, and use the back of a spoon swirl it lightly into the frosting, if desired. Slice and enjoy! Store leftovers, covered tightly, in the fridge for 3-4 days.

Make-Ahead Tips: Frosting can be made 1-2 days ahead. Cover well and store in the fridge. Let frosting sit out for 10-15 minutes, then beat it with the mixer again to get it spreadable.