Heat your oven to 350°F and line an 8x8 inch baking dish with parchment paper, allowing the paper to overhang slightly on two sides for easy removal later. This setup ensures even baking and makes it simple to lift the cooled brownies out for cutting.
In a medium bowl, whisk together the sugar, sifted coconut flour, cocoa powder, salt, and baking powder until well combined and no lumps remain. Sifting the coconut flour is crucial since it tends to clump easily, and whisking ensures the leavening agent and salt are evenly distributed throughout the dry mixture for consistent brownie texture.
In a separate bowl, whisk together the melted and cooled coconut oil, vanilla, and room-temperature eggs until well combined and slightly emulsified. Using room-temperature eggs is important because they incorporate more smoothly into the batter, creating a better texture. I find that cooling the coconut oil prevents it from cooking the eggs, which would create an uneven batter.
Gently fold the dry ingredient mixture from Step 2 into the wet ingredient mixture from Step 3 using a spatula, stirring just until combined. Be careful not to overmix, as this can develop too much gluten-like structure in coconut flour and make the brownies dense. Stop stirring as soon as no dry streaks remain.
Pour the batter into your prepared pan and smooth the top with a spatula. Bake for 16–20 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs (not wet batter). Coconut flour brownies can appear underdone but continue cooking as they cool, so err on the side of slightly underbaked for the fudgiest texture.
While the brownies cool for about 30 minutes at room temperature, prepare the frosting by combining the chocolate chips, milk, remaining 1/4 cup coconut oil, vanilla, and pinch of salt in a small saucepan over low heat. Stir gently until the chocolate melts and the frosting is smooth and glossy. Let the frosting cool for 10–20 minutes until it thickens slightly but is still pourable, then pour it evenly over the partially cooled brownies. Allow the frosting to set at room temperature for another 30 minutes before refrigerating.
Place the frosted brownies in the refrigerator for 1–2 hours until the frosting is completely set and firm. Using the parchment paper overhang, carefully lift the entire brownie block onto a cutting board. Cut into 16 squares using a sharp knife, wiping the blade between cuts for clean edges. Serve chilled or at room temperature—I find they have the best fudgy texture when served cold.