Heat the large pot over medium heat. Add the olive oil and once shimmering, add the diced onion. Cook, stirring occasionally, until the onion becomes translucent and soft, about 5 minutes. The onions should be translucent with a slight golden hue around the edges.
Add the minced garlic to the pot and cook for another 1 minute, stirring constantly. Aromatic compounds should be releasing, and the garlic will turn fragrant, slightly golden at the edges.
Pour in the canned tomatoes along with their juices. Use a spoon or spatula to break the tomatoes into smaller pieces as they cook, stirring occasionally. Continue cooking for 10 minutes, allowing the mixture to simmer and the flavors to meld. You should see the mixture thicken slightly and the tomatoes reduce in volume.
Add the vegetable broth to the pot, stirring to combine. Bring the mixture to a gentle simmer and cook uncovered for another 10-15 minutes. The soup will become richer and slightly thicker, with bubbling around the edges indicating it's ready for blending.
Use an immersion blender directly in the pot, or carefully transfer the soup in batches to a blender. Blend until completely smooth and silky, with a uniform, velvety texture. Stop blending when the soup appears glossy and well-integrated.
Return the soup to the heat if necessary, season with salt and pepper to taste, and cook for another 2-3 minutes. Once done, serve hot with optional garnishes like fresh basil or a drizzle of olive oil.
