Add crushed tomatoes, diced tomatoes, chicken broth, and minced garlic to a large pot. Stir and bring to a rolling boil over medium-high heat.
Boil for about 10 minutes, stirring regularly, until the soup reduces slightly and the garlic mellows.
Reduce heat to low. Add butter and sugar and stir until the butter melts completely.
Blend with an immersion blender if you want a smoother texture, or leave it slightly chunky.
Slowly drizzle in heavy cream while stirring constantly over low heat.
Stir in fresh basil and cayenne. Let sit on low heat for 2 to 3 minutes, then taste and adjust salt or cayenne.
Serve warm.
Notes
Add the heavy cream slowly over low heat so the bisque stays smooth. Use both crushed and diced tomatoes for body and texture. Blend only if you want a smoother soup. Add fresh basil at the end so it keeps its bright flavor.