Slice the vegetables and add them to a baking sheet. Slice the top off of the head of the garlic and add the whole head to the sheet too.
Using a basting brush, cover each vegetable in olive oil on both sides - except the garlic. Just leave the garlic cloves up.
Broil everything together for 20 minutes on the center rack of the oven.
Flip everything over and broil for another 10 minutes.
When done, the garlic should easily squeeze out of it's shell. Add those cloves to the Dutch oven.
Remove any overly roasted portions of the tomatoes and onions. Often, I end up pulling off a lot of the tomato skins because they get difficult to grind up.
Add everything to the Dutch oven and then add in the basil.
Add in the cup of water and simmer for 10 minutes, stirring frequently.
After 10 minutes, shut off the heat of the burner and use the hand blender to blend the soup for a for minutes
Once done, simmer again for another 5-10 minutes and then blend everything again to give a smoother finish. Do this until you have the consistency you like.
Add in the heavy cream and simmer for another 10 minutes.
Serve immediately with extra basil, creme fraiche, thyme, additional olive oil or additional salt and pepper to taste.