Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Slice 3 lbs of grape tomatoes in half. Peel each garlic clove from one garlic bulb. Add the tomatoes and garlic to the baking sheet. Place in the oven to bake for 30-35 minutes, until everything is soft.
Use a spatula to scoop the garlic and tomatoes into a blender or a food processor. Puree until smooth and creamy. Pour it into a large bowl temporarily and set aside.
Sautee + Blend Onions:
Heat a large pot over medium-high heat. Add a bit of cooking oil and the 1 chopped onion, ½ tsp dried thyme, 1 tsp salt and ½ tsp ground black pepper and mix together. Cook until the onion turns translucent, about 2 minutes.
Now add that cooked onion mixture, along with ½ cup fresh basil and 1 cup vegetable broth to a blender or food processor. Blend until smooth and creamy. Set aside.
Balsamic Vinegar:
Add the 2 Tbsp balsamic vinegar and 2 tsp of vegetable broth (or water) to the pot that just had the onions in it and gently stir, scraping up any bits from the bottom of the pan. Cook for one minute, until it reduces in half.
Mix Everything Together In Main Soup Pot:
Next, pour in the pureed tomato mixture and pureed basil onion mixture over top of the balsamic vinegar. Stir everything together. Heat over medium-high heat, and let simmer for 3-5 minutes.
Remove the pot from the heat and stir in ¼ cup heavy cream. Now you can scoop into bowls and serve.