Preheat the oven to 400°F. Toss the tomatoes, onion, and garlic with olive oil, spread them out on a sheet pan, and sprinkle with 1 teaspoon of salt.
Roast the tomatoes, garlic, and onion for 30 to 35 minutes, until the tomatoes are wrinkled and slightly browned.
Place 1/4 cup of the basil leaves, roasted tomatoes, onion, and garlic, chicken broth, heavy cream, salt, and pepper in a high powered blender and blend until smooth.
Pour the blended soup into a pot over medium heat on the stovetop. Once heated, turn the heat down to low and simmer for 15 minutes, scraping the bottom of the pot frequently to make sure the cream doesn't burn.
Garnish with more fresh basil and salt and pepper as desired. Serve and enjoy!