Heat oil in a large (at least 5 quart) stockpot or Dutch oven over medium-high heat. Add crumbled sausage and cook, stirring occasionally, until browned, about 10 minutes. Using a slotted spoon, transfer sausage to a plate. If you have more than 2 tablespoons fat in pot, remove excess. Add onions, carrots and celery to pot and cook, stirring frequently, until vegetables are tender but not brown, about 8 minutes (if the bottom of the pot is beginning to brown, lower heat and stir in a couple of tablespoons water) . Add garlic, rosemary, thyme, salt, black pepper, and red pepper flakes, cook until garlic is fragrant, about 1 minute. Stir in chicken stock. Add 1 can of beans to a small bowl and use a fork to mash beans into a coarse paste. Add mashed beans to pot and bring soup to a boil, reduce heat and simmer for 15 minutes, stirring occasionally.

Stir in cream cheese, escarole, cooked sausage and remaining 2 cans of beans; let simmer until escarole is wilted and tender, 10 minutes. Ladle soup into bowls and sprinkle with Parmesan cheese.