Preheat two ovens to 450°F. If you only have one oven, arrange the racks so that they're evenly spaced to accommodate a good air flow.
Lightly grease one sheet pan with extra virgin olive oil and assemble the cut tomatoes onto the pan in a single layer. Roast the tomatoes for 30-35 minutes, or until they are browned on the edges. Toss the celery, carrots, and onions in 2 tablespoons of olive oil. Nestle the head of garlic (cut side up) in a square piece of heavy-duty aluminum foil and pour the remaining olive oil over it. Tightly wrap up the garlic in the foil and place the garlic onto the pan with the veggies. Roast the veggies for 30-35 minutes as well. When roasted they should look brown and nicely caramelized.
Once the vegetables are finished roasting, transfer everything except the garlic to a dutch oven.
Pour a 1/2 cup of the chicken stock onto the sheet pans and use a wooden spoon to scrape up the browned bits from the pans. Add this liquid to the dutch oven along with the tomatoes, the veggies, and the bay leaf.
Add the sugar, salt, pepper, and the rest of the chicken stock to the pot. Bring the mixture up to a boil, and reduce the heat to low and simmer, covered, for 15 minutes.
Once the soup has finished cooking, use an immersion blender to puree the mixture*. After a few pulses with the immersion blender, take the head of garlic, and squeeze half of it into the pot, then continue blending until smooth.
Remove the pot from the heat and stir in the chopped basil and the cream. Stir the cream in well. If you're using very cold cream, you may have to return the pot to the stove and heat it until warmed through. Be sure to avoid boiling the bisque once the cream has been added.