In a large soup pot, melt butter over medium heat. Add onion, carrot, celery, and garlic and saute until veggies become soft and clear. Stir in the flour and cook for about 2 minutes.
Pour in chicken broth, whisking constantly.
Add tomatoes and bring to a boil, stirring often. Stir in pesto, oregano and sugar and reduce heat. Simmer for 30 minutes. (If using a Crock Pot, add the sauteed veggies and ingredients above to a Crock Pot and cook on low at least 4 hours. See note above)
Remove from heat and cool.
Working in batches, blend the soup in a blender until smooth.
Return to pot and heat over medium heat. Whisk in heavy cream and add salt and pepper, to taste.
Garnish with Parmesan cheese and serve.