Set your Instant Pot to 'Sauté' mode and pour in the olive oil.
Add the chopped onion and sauté for 3-4 minutes until softened.
Stir in the minced garlic and continue to sauté for another 30 seconds until fragrant.
Add the diced tomatoes (with their juices), vegetable broth, sugar, oregano, salt, and pepper. Stir well to combine.
Close the Instant Pot lid and set the valve to 'Sealing'. Select 'Manual' or 'Pressure Cook' and set it for 10 minutes.
Once the cooking time is completed, allow a natural pressure release for 10 minutes, then carefully turn the valve to 'Venting' to release any remaining pressure.
Open the lid and use an immersion blender to blend the soup until smooth. Alternatively, you can carefully transfer the soup in batches to a blender.
Stir in the heavy cream (or coconut milk) and the fresh basil leaves. Blend again briefly just to incorporate the basil.
Taste and adjust seasoning if necessary and simmer for an additional 2-3 minutes on the 'Sauté' setting if you want to warm it further.
Serve hot, garnished with additional fresh basil if desired.