In a large pot, heat the olive oil over medium heat.
Add the chopped onion and sauté until soft and translucent, about 5-7 minutes.
Stir in the minced garlic, ground black pepper, and salt, cooking for an additional minute until fragrant.
Pour the crushed tomatoes and vegetable broth into the pot. Add the sugar and dried oregano, stirring to combine.
Bring the mixture to a simmer, cover, and let it cook for 15-20 minutes, allowing the flavors to meld together.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. If you don't have an immersion blender, carefully transfer the soup in batches to a blender and blend until smooth, then return to the pot.
Stir in the heavy cream and the chopped fresh basil. Heat the soup gently until warmed through.
Taste and adjust the seasoning if necessary.
Serve hot, garnished with fresh basil leaves. Enjoy with crusty bread if desired.