Heat a drizzle of olive oil in a medium saucepan over medium heat. Add the ground garlic and sauté for 30 seconds — just long enough for the garlic to become fragrant and lose its raw edge.
Pour in the Basic Tomato Sauce. Stir to combine and bring to a gentle simmer over medium heat.
Simmer for 8 to 10 minutes, stirring occasionally. The soup should heat through and begin to concentrate slightly. This is the step that develops the flavor.
Remove the pot from the heat. Using an immersion blender, blend until the soup is completely smooth and velvety. If using a standing blender, transfer in batches — fill no more than halfway, hold the lid with a folded kitchen towel, blend on medium. Return to the pot.
Stir in the heavy cream and grated parmesan. Return to the lowest possible simmer for 2 minutes, just to warm through. Do not let it boil after the cream is added.
Taste and adjust seasoning with salt and pepper.
Ladle into bowls. Tear fresh basil leaves over the top and serve immediately with the crostini alongside.