This is not a quick and easy minestrone recipe, as it takes all day, but it is the best minestrone I've ever eaten. Make this dish on a cold, rainy or snowy day when you have all day to putter about the house. Building this soup isn't hard, but it requires a few specific steps to pull it off correctly. It makes a lot of soup, but it holds well for a week or so and can be frozen. If you want to improve it even more, drop a dollop of pesto into each bowl when you serve it. All this minestrone needs to go with it are crusty bread and a medium-bodied wine, like a Sangiovese.
Start by buzzing all the base ingredients (except the pork) in a food processor until small. You do not want a puree. Cut the pork into large pieces and put in a Dutch oven or other lidded pot. Add the chopped veggies and cover with water; you'll need at least a quart of water, maybe two. Cover and simmer for 3 to 4 hours. This can be done ahead of time.
Meanwhile, slowly cook the white beans in another pot. Do not let the water boil or the beans will burst. Gently cook the beans and they will retain their shape and get creamy. Add some salt to the water after about 30 minutes. When they are done, remove from the water and set aside.
After the base has simmered, fish out the pork and put it in the food processor. Blitz it until the meat becomes a puree; you might need to add some of the broth. Return that to the pot and mix well.
Add the tomato paste, crushed tomatoes, thyme, oregano and rosemary. Stir well, and test for salt. Add some if needed. Cover and simmer for another hour. After this time, add the carrots and the potatoes, cover and let simmer for 30 minutes. Add the cauliflower and beans, cover and cook for another 30 minutes.
Right at the end, add the turnip greens and most of the cheese (you want some cheese left over for garnish). Stir well and cook for a few more minutes, until the turnip greens are wilted.