Preheat oven to 350°F. Line your largest baking tray with a sheet of parchment.
Scatter a pint of cherry tomatoes out on the baking sheet. Add the carrots, the onion, the 2 whole shallots, and all of the garlics. Add 2 tablespoons of the olive oil, 1 teaspoon cumin, 1 teaspoon smoked paprika, 1 teaspoon dried dill, some black pepper and Kosher salt to taste. Use your hands and toss the vegetables around COATING EVERYTHING. Turn the garlic head halves upside down so their exposed flesh is against the baking sheet. Nestle the herbs in between the vegetables.
Bake for anywhere between 35 minutes to one hour. I go the full hour as I like to encourage a mild amount of charring on the vegetables. You may need to stir the contents of the baking sheet halfway through.
In a large Dutch oven, the remaining tablespoon of olive oil and heat it to shimmering. Add the celery, the 2 diced shallots, and the red onion. Sauté over medium heat for about 10 minutes until some pieces are translucent and others mildly golden. Using a wooden spoon, push all to one side of the Dutch oven. Add tomato paste directly into the space you've created. Using the same wooden spoon, 'spread' the tomato paste over the bottom half of the Dutch oven. Cook the tomato paste for several minutes before stirring it and re-spreading it. You will cook it until it browns, about 15 minutes. See my progression photos above.
Merge the now browned tomato paste with the vegetables and add in the remaining cumin, remaining dried dill, remaining smoked paprika, a pinch of red pepper flakes, and honey. Still over medium heat, begin deglazing with whatever stock you intend to use, whisking constantly and scraping any bits that accumulated on the bottom. If you intend to use a rind of an aged cheese, add it now and simmer for 20 minutes, removing and discarding after.
Remove baking sheet from the oven. Squeeze out the roasted garlic from its papery exterior. Spoon the vegetables into the Dutch oven mixture, careful to remove any vine tomatoes you may have chosen to roast and are planning to use as a garnish. Add in any juices that collected beneath the vegetables by gently lifting one end of the parchment into the Dutch oven.
Run the stems of what remain of your herbs between your thumb and forefinger removing what leaves pull away easily. Add them to the Dutch oven. If your herbs are looking scorched, simply discard them because technically, they've done their job.
Use an immersion blender to puree the mixture directly in the pot. If you do not own an immersion blender, use a very large blender or food processor that hot liquid will not damage.
If serving immediately, begin drizzling in heavy cream or coconut milk, pureeing some more after you've added it. TASTE YOUR SOUP. Season accordingly and keep warm over very low heat until you are ready to serve. Garnish with the roasted vine tomatoes.