In a large sauce pot, warm the olive oil. Add the onions and sauté for about 5 minutes. Add the garlic, tomato paste, rosemary, and salt, and sauté another 30-60 seconds.
Add remaining ingredients - diced tomatoes, balsamic vinegar, broth, and white beans - and bring to a boil, then reduce to a simmer. Simmer for about 30 minutes.
Taste and adjust seasoning, adding more salt, balsamic, or other seasonings as desired and serve! (I didn't add anything extra and it was AWESOME.) If you're not blanching your greens, now's the time to stir them in. Once wilted, remove the soup from the heat and serve.
Optional Blanch: If you would like your greens to stay bright and vibrant, you can quickly blanch them before adding them to the soup. To do this, fill a big bowl with ice and 1-2 cups water. Bring a large pot of water to a boil. Drop the greens into the boiling water and let cook for about 5-30 seconds, then quickly strain / scoop out and place in the bowl of ice water. Stir until greens are cool, then immediately remove and drain before adding to recipe.