Place a large pot or saucepan over medium heat and add the olive oil. Once the oil is warm, add the chopped onion and sauté for about 4–5 minutes, stirring occasionally, until it becomes soft, translucent, and slightly sweet in aroma. This step builds the base flavor of the soup, so don’t rush it.
Add the minced garlic to the pot and cook for about 20–30 seconds, stirring constantly. As soon as the garlic becomes fragrant, move to the next step to prevent it from burning, which can give the soup a bitter taste.
Pour in the tomatoes and broth, stirring well to combine everything. Increase the heat slightly and bring the mixture to a gentle simmer. Once it starts bubbling lightly, reduce the heat to maintain a steady simmer.
Let the soup cook for about 10–15 minutes, allowing the flavors to develop and deepen. Stir occasionally and gently press down on the tomatoes with a spoon if using fresh ones to help them break down faster.
Remove the pot from heat and carefully blend the mixture until completely smooth. You can use an immersion blender directly in the pot for convenience, or transfer the soup in batches to a regular blender. Blend until there are no chunks left and the texture is silky and creamy.
Return the blended soup to low heat. Reduce the heat to the lowest setting and slowly stir in the Greek yogurt and cottage cheese. Mix continuously to ensure they fully incorporate into the soup without curdling. This step adds creaminess and boosts the protein content.
Add the chopped fresh basil and stir it into the soup. Let it cook gently for another 2–3 minutes so the basil releases its aroma and blends into the flavor of the bisque.
Taste the soup and adjust seasoning if needed by adding a little more salt or pepper. Once everything is well combined and heated through, remove from heat and serve warm for the best creamy texture and flavor.