Preheat oven to 350 degrees Fahrenheit (177 degrees Celsius) and line a 9x9 inch pan with parchment paper. Set aside.
I suggest having all the ingredients out and measured to make this process easier.
In a bowl, whisk together the flour, cocoa powder and salt. Set aside.
If using the coffee, combine the instant coffee granules and water in a small bowl until the granules are completely absorbed. This is optional but recommended - the coffee really deepens the chocolate flavor.
In a separate, microwave-safe bowl, combine the butter and powdered sugar. Melt the two together in the microwave in 30 second increments, whisking in between each increment. I typically microwave it 4-5 times. Whisk them together until completely smooth and the powdered sugar is dissolved in the butter. It should almost look like melted white chocolate. You can also melt them together on the stove.
Meanwhile, whip your eggs. Crack the eggs in the bowl of a stand mixer fitted with the whisk attachment (or a medium sized bowl if using a handheld mixer), and beat them on medium speed for 4-5 minutes until they are a paler yellow color and foamy.
Once the eggs are done whipping, pour in the hot butter/sugar mixture. Whip them together on medium speed for two minutes. Add the vanilla and coffee mixture (if using) and whip until combined.
Add the flour, cocoa powder and salt and fold together (not whisk) until a batter forms. Whisking will knock out all of the air you just added by whipping the eggs. Pour the batter into the prepared pan.
Dollop the peanut butter onto the batter and swirl it into the top with a knife or toothpick.
Bake for 40-45 minutes (begin checking at 35 minutes - bake times vary depending on your oven). The edges will be set and a toothpick inserted into the center should come out with a few moist crumbs.
Remove the brownies from the oven and let them sit in the pan until completely cool.