Melt the butter in a large Dutch oven or heavy-bottomed pot over medium heat.
Add the diced onion and sauté until translucent and softened, approximately 5 to 7 minutes.
Incorporate the minced garlic and cook for 60 seconds until aromatic.
Stir in the tomato paste and cook for 2 minutes to develop depth of flavor through caramelization.
Add the canned tomatoes and vegetable stock, bringing the mixture to a gentle boil.
Reduce the heat to low and simmer uncovered for 20 minutes.
Using an immersion blender, process the soup until completely smooth.
Stir in the heavy cream, salt, pepper, and dried basil.
Simmer for an additional 3 minutes to incorporate flavors before serving hot.