Step 1: Sauté the Aromatics

1. Heat the olive oil or butter in a large pot over medium heat.
2. Add the diced onion and cook for 5-7 minutes, stirring occasionally, until softened and translucent.
3. Stir in the minced garlic and cook for an additional 1-2 minutes, being careful not to let it burn.

Step 2: Add the Tomatoes and Broth

1. If using canned tomatoes, pour them into the pot along with their juices. Break them up slightly with a wooden spoon. If using fresh tomatoes, peel and roughly chop them before adding.
2. Add the broth, tomato paste (if using), oregano, smoked paprika, and a pinch of salt and pepper. Stir well to combine.

Step 3: Simmer the Soup

1. Bring the mixture to a gentle boil, then reduce the heat to low.
2. Cover the pot and let the soup simmer for 20 minutes to allow the flavors to meld together. Stir occasionally to prevent sticking.

Step 4: Blend the Soup

1. Remove the pot from the heat and let it cool slightly.
2. Using an immersion blender, puree the soup until smooth. If you don’t have an immersion blender, carefully transfer the soup to a countertop blender in batches, blending until creamy.
3. Return the soup to the pot.

Step 5: Add the Cream and Basil

1. Stir in the heavy cream or half-and-half until fully incorporated.
2. Add the fresh basil leaves, tearing them slightly to release their flavor. Simmer the soup for another 5 minutes, but do not let it boil.

Step 6: Taste and Adjust

1. Taste the soup and adjust the seasoning with more salt, pepper, or a pinch of sugar if needed to balance the acidity of the tomatoes.
2. If the soup is too thick, add a splash of broth or water until it reaches your desired consistency.

Step 7: Garnish and Serve

1. Ladle the soup into bowls and garnish with fresh basil, a drizzle of olive oil or cream, and grated Parmesan cheese.
2. Serve hot with crusty bread, croutons, or a classic grilled cheese sandwich.