Heat the oil in a large pot or Dutch oven over medium heat.
Once the oil is hot, add the onions and sauté, stirring often, until translucent, 5 to 6 minutes.
Add the garlic and chopped Calabrian chilies, and continue to cook until the garlic is fragrant, 1 to 2 minutes.
Stir in the canned tomatoes (with their juice), roasted red peppers, and vegetable broth.
Season with the dried oregano, sugar (if using), salt and pepper.
Bring the mixture to a boil, then reduce heat.
Cover and simmer for 25 to 30 minutes.
Using an immersion blender, blend the soup until smooth. Alternatively, working in batches, you can transfer the soup to a high-powered blender and blend until smooth.
If you transferred the soup to a blender, transfer it back into the pot over medium-low heat.
Stir in the parmesan and heavy cream.
Continue to stir until the parmesan melts throughout.
Taste and adjust seasonings if necessary.
Serve immediately and garnish with grilled cheese croutons and fresh minced basil or parsley. Enjoy!