Heat the oil in a 3-quart pot over medium-high heat; add the turkey bacon and cook 3 minutes, stirring occasionally.
Add the onion, celery, carrot, and bell pepper and cook until starting to soften, about 3 to 5 minutes.
Turn the heat down to medium, stir in the garlic and thyme, and cook 2 minutes; stir in the flour and cook 2 minutes more.
Add the stock, tomato, tomato paste, bay leaf, oregano, salt, pepper, and beans, and bring to a boil; turn the heat down and simmer 15 minutes (uncovered). (Mash a few of the beans against the side of the pot if you want a thicker soup.)
Turn the heat off and stir in the cream and parsley.
Taste and season with additional salt and pepper as desired; serve.