Heat olive oil in a large pot over medium heat.
Add diced onion and cook until translucent, about 5–7 minutes.
Add minced garlic; cook for 1–2 minutes without browning.
Add chopped or crushed tomatoes to the pot.
Pour in broth and bring to a gentle boil.
Lower heat, cover, and simmer for 20–25 minutes.
Add basil leaves and optional sugar. Simmer for 5 more minutes.
Remove from heat and cool slightly before blending.
Blend soup using immersion blender or in batches.
Return to heat; stir in cream.
Season with salt and pepper. Simmer 5 more minutes.
Serve with croutons, basil, olive oil, or Parmesan if desired.