Place the butter and 1 tablespoon olive oil in a large saucepan over medium heat. Heat until the butter has melted and the mixture begins to sizzle.
Add the diced onion, carrot, celery, and minced garlic. Cook for approximately 5 minutes, stirring periodically, until the onion becomes translucent.
Add the whole tomatoes and their juices, water, coarse salt, black pepper, optional red pepper flakes, and dried basil to the saucepan.
Stir thoroughly, then bring the mixture to a boil. Once boiling, lower the heat and maintain a gentle simmer for 15 minutes.
Remove the saucepan from the heat and stir in the heavy cream.
Using an immersion blender, purée the soup directly in the saucepan until the consistency is completely smooth.
When using a standard countertop blender instead, process the soup in batches. Exercise caution with hot liquids, as trapped steam can force the blender lid upward. Cover the blender pitcher securely with a towel rather than sealing it tightly with the lid.
Pour the blended soup back into the saucepan. Taste and adjust with additional salt or black pepper as necessary. Return the soup to a gentle simmer if reheating is needed.
Preheat the oven to 400°F.
Place the sourdough cubes in a medium bowl. Drizzle them with 2 tablespoons olive oil and toss until the bread is evenly coated.
Arrange the cubes in one layer on a baking sheet and season with salt to taste.
Bake for 15 to 20 minutes, or until the croutons are crisp and evenly golden. Remove them from the oven and allow them to cool slightly.
Ladle the hot tomato bisque into serving bowls and finish each portion with the freshly baked sourdough croutons.