Set the Instant Pot to the 'Sauté' function. Add the olive oil and once hot, toss in the chopped onion. Sauté for 3-4 minutes until translucent. Add minced garlic and sauté for an additional minute until fragrant.
Pour in the diced tomatoes with their juice, vegetable broth, dried oregano, sugar, salt, and pepper. Stir to combine all the ingredients.
Close the lid of the Instant Pot, making sure the valve is set to 'Sealing.' Select the 'Manual' or 'Pressure Cook' setting and cook on high pressure for 10 minutes.
Once the cooking time is up, carefully do a quick release by turning the valve to 'Venting.' Once the pressure is fully released, uncover the pot.
Using an immersion blender, blend the soup until smooth. Alternatively, you can carefully transfer the soup in batches to a countertop blender, blending until creamy.
Stir in the heavy cream (or coconut cream) and chopped fresh basil. Turn the pot back to the 'Sauté' function for a few minutes to heat through. Adjust seasoning as necessary.
Ladle the soup into bowls and top with extra basil leaves for garnish.