Preheat oven to 425°F
Keep the heads of garlic in-tact by not breaking the cloves apart. Cut the top off of each head of garlic and drizzle the exposed cloves with 1 teaspoon of extra-virgin olive oil per head. Wrap each head in foil and set aside.
Rinse and halve each tomato. Arrange the tomatoes on 2 large foil-lined baking sheets. Keep a little bit of space between each tomato to allow the juices to run off. Drizzle the tomatoes with olive oil and a few pinches of kosher salt. Make room on the baking sheets for each head of garlic.
Roast the tomatoes and garlic in the oven for 30-40 minutes.
Remove each baking sheet from the oven and let cool slightly. The tomatoes will look slightly charred around the edges and liquid will pool around each tomato.
Unwrap each garlic head from the foil and remove the garlic cloves from their casings. The garlic should be soft.
Transfer the tomatoes and garlic to a food processor. Cover the food processor bowl with a lid and puree for 1 full minute. Set aside.
Prepare the roasted tomato basil soup
Melt 3 tablespoons of butter in a dutch oven or soup pot. Add the onions and saute them until they become soft and translucent.
Add the tomato paste, onion powder and garlic powder and cook for 2-3 minutes, stirring every few seconds.
Add the vodka and let the alcohol cook off (this takes about 1-2 minutes).
Add the tomato/garlic puree, heavy cream, chicken broth, and sugar. Stir and cover the pot.
Let the soup simmer over a low flame for 25-30 minutes. You can lift the lid to stir the soup every 10 minutes or so. While the soup simmers, prepare the croutons.