Prepare the Baking Pan: Preheat the oven to 350°F (175°C). Butter an 8-inch square baking pan, then line it with parchment paper. Leave enough paper hanging over the edges to create handles for lifting the brownies out after baking.
Melt the Butter Mixture: Place the unsalted butter, chopped fresh pineapple, and rum in a small saucepan. Warm over low heat until the butter has completely melted.
Blend Until Smooth: Transfer the warm butter, pineapple, and rum mixture to a food processor or blender. Process until the mixture is completely smooth and the pineapple is thoroughly incorporated.
Combine the Sugar and Flavorings: In a large mixing bowl, whisk together the granulated sugar, blended pineapple mixture, salt, and vanilla extract. The mixture will be liquid and yellow in color.
Incorporate the Eggs: Add the eggs one at a time, whisking well after each addition until fully incorporated before adding the next egg.
Add the Cocoa and Flour: Add the unsweetened natural cocoa powder and all-purpose flour to the bowl. Stir until the dry ingredients are just combined, taking care not to overmix the batter.
Fill the Baking Pan: Pour the brownie batter into the prepared square pan and spread it evenly.
Bake the Brownies: Place the pan in the preheated oven and bake for 40–45 minutes. To check for doneness, insert a toothpick into the center. It should come out with moist crumbs attached, but no wet batter.
Cool in the Pan: Transfer the pan to a wire rack and let the brownies cool for 20 minutes. This resting period allows them to settle before removal.
Remove and Finish Cooling: Use the parchment paper overhang to lift the brownies out of the pan carefully. Place them on the wire rack and allow them to finish cooling before cutting into squares.