Use a large pot to heat olive oil over medium heat. Toss in the diced onion and garlic, then cook until they turn translucent.
Blend in the tomato paste, sugar, salt, and pepper. Simmer for a few minutes to elevate the flavors.
Add the ripe tomatoes (you can cut a small "X" on the bottom of each tomato to make peeling easier). Stir well and let them simmer for about 10 minutes.
Pour in the vegetable broth and let the mixture simmer for an additional 10-15 minutes.
Using an immersion blender or transferring the mixture to a regular blender, purée the soup until smooth.
Return the soup to the pot and add the fresh basil leaves. Simmer for another 5 minutes.
If you desire a creamier texture, stir in the heavy cream at this point.
Taste and adjust the seasoning if necessary.
Serve the Fridheimar Tomato Soup hot, garnished with fresh basil leaves or a dollop of sour cream.