Puree the canned whole peeled tomatoes in a blender or food processor until smooth, then pour into a large pot.
Add chicken stock and minced garlic to the pot with the pureed tomatoes.
Heat the mixture over medium heat until it comes to a boil, then reduce heat and simmer for 2 to 3 minutes.
Taste the soup and if it has a bitter or sour flavor, stir in 1/4 to 1/2 teaspoon baking soda to balance it.
Temper the heavy cream by stirring 1/4 cup of the hot soup into the cream to prevent curdling.
Slowly add the tempered cream and grated Parmesan cheese to the pot, stirring to combine.
Bring the soup to a gentle boil again, then reduce heat and simmer for 15 minutes.
Use an immersion blender to puree the soup until it reaches a smooth and creamy consistency.
Serve the soup hot, optionally garnished with extra Parmesan cheese, grilled cheese croutons, or fresh basil.