Preheat the oven to 200°C (400°F). Grease a large baking pan with some butter or olive oil. Roughly chop the tomatoes and place them in the prepared baking pan.
Peel and roughly chop the onions. Peel and slice the garlic. Roughly chop the pepper. Place the pepper, onions, garlic, and fresh basil in the pan. You can also add a whole garlic head (this is for flavoring only; you can use the whole roasted garlic for a different recipe or spread it on some low-carb toast!).
Drizzle everything with two tablespoons of olive oil and roast for 15 minutes. Remove from the oven and give it a good stir. Roast for another 15 minutes.
When done, remove from the oven and remove whole garlic heads (if using). Transfer the vegetables to a large pan and pour in the heavy cream and broth. Add the tomato paste and sweetener. Mix well and bring to a boil. Cook for 3-4 minutes, stirring constantly.
Remove from the heat and cool for a bit. Transfer the prepared soup to a blender and pulse until completely smooth. You can also use an immersion blender for this.
Transfer the soup to serving bowls and top each with parmesan. Garnish with some fresh basil and serve immediately. Enjoy!