Preheat oven to 350°F with rack in middle position. Line an 8×8 inch pan with parchment paper, leaving 2-inch overhang on two sides for easy removal.
Combine butter and 4½ oz chopped chocolate in a microwave-safe bowl. Microwave in 15-second intervals, stirring between each, until fully melted. Set aside to cool to room temperature (still liquid, just not hot).
Add avocado to a food processor and pulse until completely smooth with no lumps. Scrape down sides, then add maple syrup and vanilla extract. Pulse until combined and set aside.
In a large mixing bowl (or stand mixer with whisk attachment), whisk eggs and brown sugar together for 1-2 minutes. The mixture should become light, fluffy, and slightly bubbly.
Add the avocado mixture to the egg mixture and whisk until just combined. Pour in the cooled melted chocolate and butter, whisking until just incorporated.
In a separate bowl, whisk together flour, cocoa powder, salt, and espresso powder (if using). Gently fold the dry ingredients into the wet mixture using a rubber spatula. Mix until just combined (don't overmix or brownies will be tough).
Pour batter into prepared pan and spread evenly with a spatula. Sprinkle the reserved 1½ oz chocolate chunks or chips over the top. Bake 21-25 minutes, until a toothpick inserted in center comes out with a few crumbs attached, not when it comes out completely clean.
Let brownies cool in the pan for at least 1-2 hours before cutting (this helps them set properly). Use parchment overhang to lift brownies out of the pan, then cut into 16 squares.
Notes
Choosing the right avocado: Use a ripe avocado that yields to gentle pressure. The flesh should be bright green, not brown. If your avocado has brown spots, cut them out before measuring.Use room temperature eggs: This helps everything combine smoothly and creates a better texture.Nutrition information: The nutrition information provided is an estimate. The calorie accuracy is not guaranteed.