Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Pour in the whole peeled tomatoes (with their juice), vegetable broth, dried oregano, salt, and pepper. Bring the mixture to a simmer.
Reduce the heat to low, cover partially, and let it simmer for 15 minutes to allow the flavors to combine.
Remove the pot from the heat. Use an immersion blender to blend the soup until completely smooth. Alternatively, carefully transfer the soup in batches to a standard blender and blend until velvety. Return the soup to the pot.
Stir in the heavy cream, chopped fresh basil, sugar (if using), and orange juice. Heat gently for 2 minutes, but do not boil after adding the cream.
Taste and adjust salt and pepper as needed before serving.
Notes
For a deeper flavor, roast the tomatoes and onion beforehand. Toss them with oil and roast at 400°F (200°C) for 20 minutes before adding them to the pot.
Serve this bisque hot with a classic grilled cheese sandwich for dipping.
If you prefer a thicker bisque, simmer uncovered for an extra 5 minutes before blending.