Add olive oil to a large heavy bottomed pot and heat over medium. When oil is shimmering, add diced sweet onion and stir to coat with oil.
Add a pinch of salt and saute over medium until onion softens and begins to caramelize (about 10minutes).
Add minced garlic to the pan and saute a few minutes longer until fragrant.
Add diced tomatoes, tomato paste, 4 cups of bone broth, salt bay leaf and basil, and bring to a boil.
Reduce heat and let simmer for 45 minutes.
Remove bay leaf. Then, using a high-speed blender or immersion blender, puree the soup until smooth.
Adjust the thickness by adding additional bone broth, if desired. If soup is too thin, allow to simmer uncovered for another 30 minutes.
Taste for salt and pepper, and top with fresh basil.