Step 1: Heat olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat.
Step 2: Add the diced onion and sauté for 5-7 minutes until translucent and softened. Do not brown.
Step 3: Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 4: Stir in the crushed San Marzano tomatoes, vegetable or chicken broth, and optional tomato paste. Mix well.
Step 5: Season with dried oregano, sugar (if using), salt, and black pepper. Bring the soup to a gentle simmer, then reduce heat to low, cover, and cook for 20-30 minutes to allow flavors to meld.
Step 6: Remove the pot from the heat. Using an immersion blender, blend the soup until completely smooth. Alternatively, carefully transfer in batches to a standard blender and process until smooth, then return to the pot.
Step 7: Stir in the heavy cream (or coconut milk). Taste and adjust seasonings as needed, adding more salt, pepper, or sugar if desired.
Step 8: Stir in the freshly chopped basil leaves. Let them wilt in the hot soup for 1-2 minutes.
Step 9: Ladle the hot tomato basil soup into bowls. Garnish with additional fresh basil, a swirl of cream, or grated Parmesan cheese, and serve immediately.