Blanch green beans in boiling water until tender, approximately 3 minutes. Remove beans from heat and submerge in an ice water bath.
For the vinaigrette, put EVOO, balsamic, brown sugar, salt, pepper and 1/2 cup blueberries in food processor. Pulse until blueberries are puréed.
Drain green beans and mix with the remaining blueberries in a salad bowl. Drizzle vinaigrette over beans and berries. Top with shaved parmesan.