Cook the edamame per the instructions and set aside to cool.
Once cooled, add the edamame to the bowl of a high-speed food processor with all the other ingredients EXCEPT the water. Bend until smooth, then add the water little by little to thin out the hummus as needed (you may need more or less).
Taste the hummus to check for seasoning, adding more lemon juice or olive oil as needed. To serve, spoon the hummus onto a bowl or platter, using a spoon to make a swoop in the center of the dish. Garnish with olive oil before serving.