Cook the turkey bacon: In a large pot or Dutch oven over medium heat, cook the diced turkey bacon until crisp and browned, about 5 minutes. Remove it with a slotted spoon and set aside, leaving the rendered fat in the pot.
Soften the vegetables: Add the onion, carrots, and celery to the pot and cook, stirring occasionally, until the onion turns translucent and the vegetables soften, about 6 minutes.
Add garlic and seasoning: Stir in the garlic and Italian seasoning and cook just until fragrant, about 30 seconds, being careful not to let the garlic burn.
Stir in the savory swap: Add the soy sauce and rice vinegar, stirring to coat the vegetables; this stands in for Worcestershire sauce and adds savory depth to the broth.
Add tomatoes and beans: Pour in the diced tomatoes and cannellini beans, then stir to combine everything in the pot.
Pour in the broth: Add the beef broth and bring the pot to a gentle boil, then reduce the heat and let it simmer uncovered for 15 minutes so the flavors meld.
Mash some beans: Use the back of a spoon to mash a few beans against the side of the pot, which thickens the broth naturally without adding cream.
Cook the pasta: Stir in the ditalini pasta and simmer until just tender, about 9 minutes, stirring occasionally so it doesn't stick to the bottom of the pot.
Return the turkey bacon: Stir the cooked turkey bacon back into the pot and season the soup with salt and black pepper to taste.
Rest before serving: Let the soup sit off the heat for 5 minutes to thicken slightly, then ladle into bowls and top with Parmesan cheese and fresh parsley.