Preheat your oven to 425 °F then line a large baking sheet with aluminum foil.
Prepare the vegetables. Halve the Roma tomatoes, or cut particularly large tomatoes into quarters. Slice the red bell pepper into four even pieces and quarter the yellow onion. Arrange the tomatoes, bell pepper, onion, and fresh thyme on the prepared baking sheet. Drizzle with olive oil, season with salt and pepper, and toss until everything is evenly coated.
Trim just enough from the top of the garlic head to expose the tips of the cloves. Nestle the whole garlic head among the vegetables. Drizzle the exposed cloves with a little olive oil and season with salt and pepper.
Roast for 45–50 minutes, or until the vegetables are tender and the tomatoes have begun to char around the edges.
Remove the baking sheet from the oven.Transfer the roasted vegetables to a large Dutch oven. Squeeze the roasted garlic cloves from their skins directly into the pot, using a fork to remove any stubborn cloves. Add the fresh basil and 3 cups of chicken broth. Blend with an immersion blender for about 5 minutes, or until completely smooth. Alternatively, carefully blend everything in a countertop blender.
For a thinner soup, gradually add up to 1 additional cup of chicken broth until it reaches your preferred consistency.
Place the Dutch oven over medium-low heat and bring the soup to a gentle simmer. Stir in the heavy cream and continue cooking until warmed through.
Taste and adjust the salt and pepper as needed.
Drizzle each bowl with a small spoonful of heavy cream, if desired.
Serve topped with croutons or with a grilled cheese.