Chop the large yellow onion into roughly 1-inch pieces. No need for perfect dice—just small enough to soften evenly.
Mince three cloves of garlic finely, releasing their fragrant aroma as you work.
Pour two tablespoons of olive oil into a skillet and heat over medium heat until shimmering. Add the chopped onion and minced garlic, sautéing until fragrant and translucent, about 5 minutes. The onion should be soft and slightly golden, and the garlic will smell aromatic.
Transfer the sautéed onion and garlic into the slow cooker. Add the two cans of whole peeled tomatoes with their juice, two cups of vegetable broth, and a teaspoon of sugar. Stir everything together to combine.
Set the slow cooker to low and cook uncovered for 4 to 6 hours. During this time, the tomatoes will break down and release a rich, savory aroma. The mixture should become thick and bubbling gently.
Once cooked, carefully use an immersion blender to puree the soup directly in the slow cooker until smooth and velvety. Alternatively, transfer the mixture in batches to a blender, blending until silky, then return to the slow cooker.
Taste the soup and adjust seasoning as needed. Stir in a splash of cream or milk for added richness, giving the soup a silky, inviting texture. If too thick, add a little hot broth or water to loosen it up.
Pour the hot tomato soup into bowls. Finish with a drizzle of olive oil or a dollop of cream if desired. Serve immediately to enjoy its warm, comforting aroma and smooth, velvety texture.
