
Preheat oven to 350°F. Line a 9 x 9 inch or 8 x 8 inch square pan with parchment paper. To make it easier to remove the brownies later, have an overhang of parchment paper over the edges of the baking pan. Use butter to stick the paper to the pan. Set aside when done.
Place the butter in a heat-proof bowl and microwave to completely melt the butter, and until the butter is fairly hot.
Add the brown sugar, white sugar, and salt while the butter is still hot. Mix to combine the butter and sugars together until you have a smooth paste.
Add the vanilla, coffee extract (if using), eggs, and egg yolks to the butter-sugar mix. Mix in the eggs until they have been incorporated into the butter-sugar mix.
Using a hand mixer, whisk the butter-sugar-egg mix on medium high speed, until the batter becomes pale in color (3 - 4 minutes) and is thick. This is an important step.
In a separate bowl, sift the flour and cocoa powder together.
Add the flour-cocoa mix into the wet ingredients (in two batches if that's easier) and mix it in until just combined. DO NOT OVERMIX. Add the chopped chocolate halfway through the mixing in of the flour. The goal is to make sure the batter is not overmixed when the flour is being incorporated.
Scrape the batter into the prepared pan. Evenly spread the batter. Sprinkle the remaining chocolate on top (optional). You may not need to use all of the chocolate.
Bake for 30 - 40 minutes (30 minutes = extra fudgy, 35 minutes = perfectly fudgy for my liking, 40 minutes = fudgy, but not gooey at all). Slightly longer times for an 8 x 8 inch pan. For fudgy brownies, the internal temperature in the middle should be about 206°F and 213°F about 1 inch from the edge of the pan.
Remove from the oven and let it cool down to room temperature. Remove the brownies from the pan and let them chill in the fridge for a couple of hours (chilled brownies are easier to cut).
Cut the brownies into 16 pieces. Use a warm knife to cut, making sure to clean the blade after each cut for clean and neat edges.