In a large pot over medium heat melt the butter. Add the onions and continue cooking until they become soft and somewhat translucent, while stirring frequently so not to burn them. Add the garlic and cook for an additional minute. Garlic burns very quickly.
Add the tomatoes, chicken broth, basil, sugar, and black pepper. Stir well, and bring to a boil.
Reduce heat to low, and simmer with a lid cracked for 10 minutes, while stirring occasionally.
Remove pan from the heat and let cool slightly.
f you have an immersion blender, blend the soup in the pot until smooth. If you do not own one, transfer the soup to a blender and pulse until smooth. Depending on the size of your blender, you may need to do this in batches. Be careful not to fill the blender too much before blending. Once smooth, transfer the soup back to the original pot.
Add the heavy cream and a 1/3 cup parmesan cheese, and return to a simmer for 10 minutes.
Serve as is, or top with a little chopped basil and parmesan cheese.