Preheat oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, allowing it to overhang slightly on two sides for easy removal. This takes about 2 minutes.

In a small mixing bowl, whisk together 2 cups all-purpose flour, 1 cup unsweetened cocoa powder, 2 teaspoons baking powder, and 1 teaspoon salt. Whisk for 1 minute until evenly combined and no cocoa lumps remain. Checkpoint: The dry mixture should be uniform brown with no visible cocoa pockets.

In a large saucepan, combine 1 cup unsalted butter and 2 cups granulated sugar over low heat. Stir constantly for 4-5 minutes until the butter is completely melted and sugar is fully dissolved. The mixture should look smooth and slightly shiny, not gritty.

Remove the saucepan from heat and let cool for exactly 5 minutes. This prevents the eggs from cooking when added.

Add 4 large eggs to the cooled mixture, one at a time, beating vigorously with a wooden spoon or whisk for about 30 seconds after each addition. After the 4th egg, the mixture should look thick, glossy, and slightly pale.

Stir in 2 teaspoons vanilla extract. Mix for 30 seconds until fully incorporated.

Add 3/4 cup creamy peanut butter to the mixture. Stir slowly at first to combine, then beat for 1-2 minutes until the peanut butter is fully blended and no streaks remain. The batter should look smooth and evenly colored.

Gradually add the dry ingredient mixture to the wet mixture in three additions. After each addition, fold gently with a spatula for about 20-30 seconds until just combined. Do not overmix. After the final fold, the batter should look smooth with no visible flour streaks. Checkpoint: The batter is ready when you see no dry flour and no lumps remain.

Pour the batter into your prepared 9x13 inch baking pan. Spread it evenly to all corners using an offset spatula or the back of a spoon, which takes about 1 minute.

Place the pan on the middle oven rack and bake for 20-22 minutes. The brownies are done when a toothpick inserted into the center comes out with just a few moist crumbs (not wet batter). The edges should look slightly set and the top should feel firm but still have a slight jiggle in the center when you gently shake the pan.

Remove the pan from the oven and place on a wire cooling rack. Let cool in the pan for exactly 15 minutes at room temperature. This allows the brownies to set slightly so the filling doesn't sink in.

While the brownies cool, make the peanut butter filling: In a medium bowl, combine 1/2 cup smooth peanut butter, 1/4 cup powdered sugar, 2 tablespoons unsalted butter (softened), and 1/4 teaspoon salt. Beat together for 1-2 minutes using an electric mixer or wooden spoon until light, fluffy, and completely smooth. The mixture should be spreadable and look creamy. Checkpoint: The filling is ready when it's smooth throughout with no lumps or streaks.

Once the brownies have cooled for 15 minutes, carefully spread the peanut butter filling evenly over the entire top layer in an even 1/4-inch thick layer. Use an offset spatula, wiping it clean between strokes to keep edges neat. This takes about 2 minutes.

Place the filled brownies in the refrigerator for 10 minutes to allow the filling to firm up slightly.

While the brownies chill, prepare the chocolate drizzle: Place 1/2 cup semi-sweet chocolate chips and 1 tablespoon coconut oil in a microwave-safe bowl.

Microwave the chocolate mixture on 50% power in 30-second intervals, stirring well between each interval. After the first interval, stir—the chocolate will still look mostly solid. After the second interval at about 60 seconds total, stir again. By the third interval (around 90 seconds), most chocolate should be melted. Stop microwaving when just a few small pieces remain and the mixture is smooth and glossy when stirred. Do not overheat or the chocolate will become thick and grainy. The melted chocolate should be thin enough to drizzle but not so hot it's smoking. Checkpoint: The chocolate is ready when it's completely smooth, glossy, and thin enough to pour but thick enough to hold its shape briefly.

Remove the brownies from the refrigerator. Using a fork or small whisk, drizzle the melted chocolate in thin lines across the top of the peanut butter layer in a decorative crosshatch or wavy pattern. This creates an attractive presentation and takes about 2 minutes.

Allow the chocolate drizzle to set at room temperature for 20-30 minutes until it's completely firm and no longer tacky to the touch. If you want to speed this up, place the pan in the refrigerator for 10 minutes.

Once the chocolate is set, use the parchment paper overhang to carefully lift the entire brownie slab from the pan onto a cutting board. Discard the parchment.

Using a sharp knife, cut the brownies into 12-16 pieces (depending on desired size). For clean cuts, wipe the knife blade clean with a warm, damp cloth between each cut. The brownies should cut cleanly with distinct layers visible.

Serve immediately at room temperature or store in an airtight container. Each brownie should show three distinct layers: dark fudgy chocolate on bottom, creamy tan peanut butter in the middle, and chocolate drizzle on top.