Begin the brownie recipe by adjusting your oven rack to the middle position and preheat the oven to 350 degrees F.
Line an 8.5 by 4.5-inch loaf pan with parchment paper or aluminium foil. If using foil, spray with non-stick cooking spray as well to ensure the release of your brownies.
In a small bowl combine the 3 ½ ounces semisweet chocolate, 4 tablespoons butter, and 1 tablespoon unsweetened cocoa powder and place in the microwave by setting on 30-second intervals at a time until the chocolate begins to melt, then remove and stir until the mixture is smooth. Set aside and allow to cool a bit.
In a separate small bowl, whisk together the ½ cup granulated sugar, 2 tablespoons granulated sugar, 1 large egg, 1 large egg yolk, 1 teaspoon vanilla extract, and 1 teaspoon salt until combined.
Then whisk in the chocolate mixture until combined. Stir the ½ cup all-purpose flour using a rubber spatula until combined. Transfer the brownie mixture to the prepared pan and level off the surface with a small spatula or spoon.
Place into the oven and bake for 15 to 20 minutes, until a toothpick comes out clean. You may need to rotate the pan halfway through baking.
Allow the brownies to cool in the pan completely before removing them. Then lifting the brownies out using the edges of the paper or foil, cut the brownies into small squares. Enjoy!
These fudgy brownies from scratch can be stored in an airtight container or plastic storage bag at room temperature for up to 5 days.