In a large, heavy pot or Dutch oven, boil the first 6 ingredients and 3 cups water for 2 minutes. Reduce heat to low, cover and cook, stirring occasionally, until the beans are tender, 2 1/2 to 2 3/4 hours, adding 1/4 cup more water at a time as needed. Season with salt and pepper.
Add the tortellini, increase the heat and bring to a boil. Cover, reduce the heat to low, and simmer until the tortellini is cooked through, about 10 minutes; season.
Divide the soup among shallow soup bowls. Sprinkle with the cheese. Garnish with the parsley and drizzle with EVOO.