Add the butter beans, garlic, lemon zest and juice and 3 tablespoons of the olive oil to the carafe of a food processor. Pulse until a smooth paste is formed, about 1 minute. With the machine running, drizzle in 1/4 cup water and process until the desired texture is reached. Add the basil, dill, parsley, vinegar, salt and pepper. Process until the herbs are incorporated into the dip.
Pour the dip into a serving bowl. To garnish, drizzle with the remaining 1 tablespoon olive oil and sprinkle with parsley leaves. Serve the dip alongside fresh crudite and toasted bread for dipping or store in an airtight container, refrigerated, for up to 1 week.