Special equipment: an immersion blender
Preheat the oven to 400 degrees F and line a baking sheet with parchment paper.
Place the tomatoes cut-side up in a single layer on the baking sheet. Drizzle with 1/4 cup olive oil and sprinkle with 1 teaspoon salt, 1/4 teaspoon pepper and the sugar. Scatter the thyme sprigs over the tomatoes. Roast until the tomatoes are wrinkled and soft, about 1 hour. Let cool until cool enough to handle. Discard the thyme sprigs. Gently peel off and discard the tomato skins.
Heat the remaining 2 tablespoons olive oil in a large Dutch oven over medium heat. Add the onions and a pinch of salt and cook until the onions start to lightly brown around the edges, about 3 minutes. Add the garlic and cook until fragrant, about 1 minute. Add the tomatoes, vegetable stock and bay leaf and simmer, partially covered, for 30 minutes. Reduce the heat to low, add the cream and chopped basil and simmer for 5 more minutes. Remove the bay leaf and use an immersion blender to puree the soup until smooth. Season to taste with about 2 teaspoons salt and some freshly ground black pepper.
When ready to serve, top with a drizzle of chile-infused oil and garnish with some basil leaves.