Begin by setting your Instant Pot to the 'Sauté' function. Pour in the olive oil and let it heat up. Once hot, add the chopped onion. Sauté this mix for 3-4 minutes until the onion is translucent and soft. Next, introduce the minced garlic and cook for an additional minute, stirring frequently until it releases a wonderful aroma.
Carefully pour in the diced tomatoes, ensuring to include their juices for added flavor. Then, add the vegetable broth, dried oregano, sugar, salt, and pepper. Stir all the ingredients together until they are well combined.
Close the lid of the Instant Pot, ensuring the valve is switched to 'Sealing.' Select the 'Manual' or 'Pressure Cook' setting and set the timer for 10 minutes on high pressure.
When the cooking time has elapsed, perform a quick release by turning the valve to 'Venting.' Wait until all the steam has escaped, then carefully remove the lid from the pot.
Using an immersion blender, blend the soup directly in the pot until it reaches a smooth, creamy consistency. If you prefer, you can also transfer the hot soup in batches to a countertop blender, blending each batch until creamy. Be cautious, as the soup will be very hot.
Stir in the heavy cream (or coconut cream) and add the chopped fresh basil to the blended soup. Switch the Instant Pot back to the 'Sauté' function for a few minutes to gently heat the soup through. Taste and adjust the seasoning if needed, adding more salt and pepper as desired.
Carefully ladle the soup into warm bowls and garnish with additional fresh basil leaves for an aromatic touch.