In a large pot, warm the beef stock and keep it warm with a lid on.
Drain the tomatoes, reserving the juice. Add the juice to your stock.
In a large, heavy bottomed soup pot over medium heat, add the bacon and olive oil. Cook until bacon is crisp. Remove bacon bits to a paper-towel lined plate. To the bacon fat and oil, add the onion, carrot and celery and cook for about 8 minutes, stirring occasionally until the vegetables are softened.
Add the rice, garlic, salt, rosemary and oregano. Cook and stir for about 2 minutes to toast the rice a bit.
Add about 1 1/2 cups of the beef stock and tomato juice mixture. Stir well, cover and simmer for about 10 minutes. Remove lid, stir the rice mixture a few times and add another 1 1/2 cups of broth. Stir again, cover, and simmer again for 10 minutes. You may need to turn your heat to medium-low so it's not cooking too fast. Remove the lid a third time and stir well. Add the remaining stock and tomato juice. Stir and allow to simmer until most of the liquid is absorbed, 10 -15 minutes. Remove lid and stir in the drained tomatoes and beans. Stir well and allow to simmer with the lid off for an additional 5 minutes.
Served the minestrone topped with plenty of fresh-grated Parmesan cheese and the reserved bacon bits.