Preheat your oven to 425°F (220°C). Arrange the quartered tomatoes on a baking sheet lightly coated with olive oil. Drizzle additional olive oil over the top and toss to ensure the tomatoes are evenly coated. Season generously with kosher salt and black pepper.

Roast the tomatoes for 20 to 40 minutes, depending on their size and moisture content, until they appear wrinkled, caramelized, and fork-tender. Once roasted, remove from the oven and allow them to cool slightly.

Transfer the roasted tomatoes to a blender, reserving any juice left on the baking sheet. Blend until smooth or to your preferred texture. Measure out 3 cups of purée. If needed, top off with a bit of tomato sauce to reach the full amount. Strain the reserved juices to yield 1 cup of clear tomato liquid.

In a large saucepan, heat 2 teaspoons of olive oil over medium-high heat until shimmering. Add the chopped onion and minced garlic. Lower the heat to medium and sauté for about 30 seconds or until aromatic and softened.

Pour in the tomato purée and the strained tomato juice. Add the chicken broth, dark brown sugar, salt, and black pepper. Stir to combine and bring the soup to a rolling boil. Allow it to boil for 10 minutes before reducing the heat to a gentle simmer.

Stir in the heavy cream and let the soup continue to simmer for another 10 to 15 minutes, allowing the flavors to meld and the soup to thicken slightly. Stir occasionally to avoid scorching.

While the soup simmers, prepare your grilled cheese croutons. Sandwich fresh mozzarella slices between two pieces of baguette. Lightly butter the outer sides of each sandwich. In a skillet set over medium heat, toast each side until the bread turns golden and crisp and the cheese is melted through.

Remove from the skillet and place on a cutting board. Let them cool briefly, then slice into bite-sized cubes, approximately ½ to 1 inch in size.

Ladle the hot soup into bowls. Garnish with a sprinkle of freshly chopped basil and top with a handful of grilled cheese croutons. Serve immediately and enjoy the comforting, creamy richness with every spoonful.