Preheat the oven to 375 degrees.
Place sliced Roma Tomatoes on a baking sheet. Drizzle with 3 tbsp. Basil Olive Oil, ensuring even coverage. Season with Kosher Salt and Ground Black Pepper. Roast in the oven for one hour.
In a Dutch oven, heat 2 tbsp. Butter and 2 tbsp. Basil Olive Oil. Add diced Yellow Onion and cook until softened.
Add minced Garlic and Fresh Thyme to the onions, stirring until fragrant.
Pour in the crushed San Marzano Tomatoes, chopped Fresh Basil, Sugar, Kosher Salt, and Ground Black Pepper. Stir to combine.
Add Chicken Stock and bring the mixture to a simmer. Let it cook for 30 minutes.
Use an immersion blender to puree the soup until smooth.
Stir in Heavy Cream, ensuring it is fully incorporated.
In a separate pan, make cheese toasts by placing American Cheese slices on thick bread slices. Toast until the cheese is melted and bubbly.
Ladle the soup into bowls, garnish with additional fresh basil, and serve with cheese toasts on the side.