Heat the oven to 350°F. Line the baking pan with parchment paper or coat it lightly with grease to prevent sticking and make the cooled brownies easier to remove.
Pass the unsweetened cocoa powder through a fine-mesh sieve directly into a large mixing bowl. Sifting breaks apart any cocoa lumps and helps the powder blend evenly into the brownie mixture.
Add the unsweetened applesauce and peanut butter to the sifted cocoa. Stir vigorously for approximately 1–2 minutes, continuing until the mixture is smooth and uniform with no visible streaks of cocoa or peanut butter.
Add most of the vegan semi-sweet chocolate chips to the prepared batter, setting aside approximately 2 tablespoons for the topping. Using a spatula or wooden spoon, gently fold the chips through the mixture only until they are evenly dispersed.
Transfer the brownie batter to the prepared baking pan and use a spatula to spread it into an even layer. Scatter the reserved chocolate chips evenly over the surface.
Place the pan in the preheated 350°F oven and bake for 25–35 minutes. The brownies are ready when the surface appears set while the middle retains a slight jiggle when the pan is gently moved.
Begin checking for doneness at the 25-minute mark by inserting a toothpick into the brownies. A few moist crumbs clinging to the toothpick indicate a fudgy interior. If wet, uncooked batter remains on the toothpick, continue baking for another 3–5 minutes before checking again.
Remove the pan from the oven and leave the brownies to cool in the pan on the counter for 10 minutes. This brief resting period allows them to become firm enough for easier handling.
Transfer the brownies to a wire cooling rack and allow them to cool completely for at least 1 hour before cutting. Waiting until they are fully cooled helps prevent crumbling and produces cleaner slices.