Preheat the oven to 375 degrees F.
Slice the tomatoes in half and place them in a roasting pan. Drizzle with olive oil, season with salt, and place into preheated oven. Roast for 40-45 minutes until the tomatoes are softened and slightly browned.
In a medium saucepan, heat butter over medium heat. Add onions and garlic and sauté for 3-4 minutes until onions are softened.
Add the roasted tomatoes to the pot and stir to combine. Add the chicken or vegetable broth, oregano, sugar, salt, and pepper. Increase the heat to medium-high and bring to a simmer. Reduce the heat to low and let simmer for 30 minutes.
Turn off the heat and allow the soup to cool slightly. Using an immersion blender, blend the tomatoes until they’re completely puréed.
Stir in the heavy cream. Simmer for 5-7 minutes until the cream has been incorporated.
Serve with a dollop of Greek yogurt and crusty bread.