Preheat oven to 325° F. Line a 9x13x2 baking pan with parchment or oiled aluminum foil. Set aside.
Whisk the dry ingredients for the brownie together in a small bowl.
In a separate bowl, mix eggs, oil, applesauce and vanilla extract. Once blended, stir in the dry ingredients and water and mix until smooth. Use either a hand mixer, stand mixer with paddle attachment or mix by hand.
Spread the brownie batter evenly in the prepared pan.
Clean the mixing bowl and switch to the whisk attachment if using a stand mixer.
Whisk all the pumpkin ingredients until smooth and any lumps have been incorporated.
Spoon dollops of pumpkin batter on top of the brownie layer.
Using a butter knife or spatula, cut through the pumpkin layer in lines, starting at one end of the pan and cutting a line all the way to the other end, and repeating across the whole pan.
Turn the pan to repeat the process in a perpendicular direction. There is no right or wrong here: you can even just use the knife to draw swirly patterns instead. The deeper you cut through the batter with the knife, the deeper the pumpkin layer will be incorporated into the brownie. If you want more of a solid layer of pumpkin on top, don’t cut so deep.
Bake in preheated oven for approximately 65 minutes, or until the center is no longer jiggly and a toothpick inserted into the brownies comes out with a few crumbs, but not wet.
Cool in the pan on a wire rack. Once cooled, lift the parchment or foil with the brownies out of the pan to cut and serve. Use a pizza cutting wheel or plastic knife to cut brownies for cleanest cut.