Preheat the oven to 350°F. Line an 8x8x2 baking pan with parchment paper “slings” going both ways. There should be overhang on both sides. Grease the parchment paper thoroughly with oil.
In a medium saucepan, combine the peanut butter, applesauce, maple syrup, and all but 3 tablespoons of the chocolate chunks. Place the saucepan over medium heat and stir with a spatula until all of the chocolate is melted, about 4-5 minutes. Stir in the vanilla extract and remove the saucepan from the heat. Let the peanut butter mixture cool slightly.
In a medium bowl, combine the cocoa powder, coconut flour, baking soda, and salt. Whisk to combine.
Once the peanut butter mixture is slightly cooled, add the cocoa powder mixture to the saucepan. Using the spatula, mix everything to combine. The batter will be thick!
Scrape the brownie batter into the prepared pan and spread it out evenly, smoothing the top with your spatula. Then, drizzle some drippy peanut butter on top and drag a paring knife through the top of the brownies to create a swirl effect. The batter is quite thick, so you have to be quite deliberate. Press the remaining chocolate chunks into the top and sprinkle with flaky sea salt if you like.
Bake the brownies until firm and slightly dry on top, about 27-30 minutes. Let them cool completely, for at least 2 hours, before slicing into squares. Store brownies covered in the refrigerator for up to 5 days.