With the oven rack in the middle position, preheat oven to 350 degrees F. Line an 8 x 8 inch square pan with enough parchment paper to create an overhang of at least two inches on two sides.
Combine the butter and 4 1/2 ounces of chopped chocolate or chocolate chips (reserve the remaining 1 1/2 ounces for the topping) in a bowl and microwave for 15 second intervals, stirring in between intervals. Continue until the butter and chocolate have melted. Set aside and let cool completely.
In a medium sized bowl, combine the flour, cocoa powder, espresso powder, and salt. Set aside.
Pulse the avocado in a food processor until smooth.*** Scrape down the sides and add the maple syrup and vanilla.
In the bowl of a stand mixer with the whisk attachment **** whisk the eggs and brown sugar for 1-2 minutes until the mixture is light, fluffy and a bit bubbly. Add the avocado mixture and whisk until just combined followed by the melted, cooled chocolate and butter mixture.
Remove the bowl from the stand and carefully fold in the dry ingredients with a rubber spatula until just combined.
Pour the mixture in the pan and use a spatula to spread it out evenly. Bake 20-25 minutes or until a toothpick comes out with crumbs (not wet, goopy batter). Do not wait to take it out when a toothpick comes out with no crumbs.
Let brownies cool completely in the pan (3-4 hours) before cutting into bars.