Combine water, sugar, cocoa, espresso powder (if using), and salt in small saucepan. Bring to simmer over medium heat and cook, stirring occasionally, until sugar and cocoa dissolve, about 2 minutes.
Remove saucepan from heat and add vanilla.
Scoop flesh of avocados into food processor bowl fitted with a blade. Process until smooth, about 2 minutes. Scrape sides as needed.
While processor is running, slowly add a steady stream of the warm cocoa mixture into the pureed avocado. After about 2 minutes, the mixture should be glossy and smooth.
Place chopped chocolate in a microwave safe container, and cook at 50 percent power or in 30 second intervals until completely melted. May take 2-4 minutes.
Add melted chocolate to avocado mixture (removed lid to add). Process for at least a minute until all ingredients are well incorporated.
Transfer to a clean bowl, and cover. Refrigerator until chilled, at least 2 or up to 24 hours.
Garnish and serve as desired.