Preheat the oven to 375 F. Line a rimmed baking sheet with parchment paper.
Cut the tomatoes in half, and remove the cores. Place the tomatoes, cut side up, onto the prepared baking sheet. Lightly drizzle olive oil over the tomatoes, then sprinkle each of them with salt and pepper. Roast for 30 minutes at 375 F. Remove from the oven, and set aside.
Warm one tablespoon of olive oil in a saucepan over medium heat. Add the chopped onion with a pinch of salt, and cook until lightly browned, about fifteen minutes. Stir in minced garlic, and cook for one minute.
Once the tomatoes are cool enough to handle, remove the skins.
Add peeled tomatoes, chicken broth, light brown sugar, dried basil, and greek seasoning to the saucepan. Stir to combine, then bring to a boil.
Turn the heat back down to a simmer, and simmer for 20 minutes.
Use an immersion blender or regular blender*** to blend the soup until smooth in texture. Turn off the heat, and stir in the half and half. Season with salt and pepper to taste, if necessary.