Preheat the oven to 325°F (165°C). Lightly grease a 9 x 13-inch baking pan or line it with parchment paper.
Place the butter, granulated sugar, cocoa powder, and salt in a large microwave-safe bowl. Stir briefly to combine.
Microwave the mixture on high for about 1 minute. Stir thoroughly until the butter has completely melted and the ingredients form a smooth chocolate mixture. If needed, microwave for another 15–20 seconds.
Allow the mixture to cool slightly if it feels very hot. Add the eggs one at a time, stirring thoroughly after each addition until completely incorporated.
Stir in the vanilla extract.
Add the all-purpose flour. Fold and stir just until no dry streaks of flour remain and a thick, smooth batter forms. Avoid excessive mixing once the flour is incorporated.
Spread the batter evenly into the prepared baking pan, smoothing the surface.
Bake the Fudgy Brownies Recipe for approximately 28–32 minutes. Start checking near the lower end of the baking time. A toothpick inserted near the center should have moist crumbs attached rather than wet batter.
Place the pan on a cooling rack and allow the brownies to cool completely, ideally for about 1 hour.
Slice into squares and serve.