Heat olive oil in a big, heavy pot over medium heat.
Toss in the diced onion and cook, stirring now and then, for about 5 minutes until it turns translucent.
Add the garlic and let it sizzle for about a minute, just until it smells amazing.
Pour in the canned tomatoes—juice and all—then add salt, sugar, and white pepper.
Let it simmer over medium heat for 15 minutes, stirring occasionally.
Pour in the chicken broth and bring it up to a gentle boil. Lower the heat and let it simmer another 10 minutes.
Add the chopped basil. Use an immersion blender to puree the soup right in the pot until it’s smooth (or carefully blend in batches if you prefer—just watch out for hot splatters!).
Turn the heat to low and slowly stir in the heavy cream until the soup is warmed through.
Give it a taste and add more salt or pepper if you think it needs it.
Ladle the hot bisque into bowls. Top with extra basil or a swirl of cream if you’re feeling fancy.