Add the chopped fresh tomatoes and vegetable broth to the pot. Bring to a simmer, cover, and cook for 25 minutes.
Remove the pot from the heat. Use an immersion blender to puree the soup until completely smooth.
Stir in the heavy cream, fresh basil, and black pepper. Keep the bisque warm over low heat.
Heat a separate skillet over medium heat. Assemble sandwiches with bread and cheese, and grill on both sides until golden brown and the cheese is completely melted.
Ladle the warm creamy tomato bisque soup into bowls. Serve immediately alongside the grilled cheese sandwiches and crispy beef bacon.