Heat a large pot over medium heat and add a drizzle of olive oil. Add the diced yellow onion, carrot, and celery. Cook for 5 to 7 minutes, stirring occasionally, until the vegetables begin to soften.
Add the minced garlic and tomato paste. Stir well and cook for 1 to 2 minutes, allowing the tomato paste to deepen in color and the garlic to become fragrant.
Add the San Marzano tomatoes and chicken stock. Use a wooden spoon to break up the tomatoes as they cook. Season with salt and pepper, then add the fresh basil.
Bring the soup to a gentle simmer. Cover partially and let it cook for 20 to 25 minutes, or until the vegetables are completely tender and the flavors have come together.
Remove the pot from the heat and use an immersion blender to blend the soup until smooth and creamy. If using a countertop blender, blend in small batches and carefully vent the lid for the hot steam.
Return the soup to low heat and add in your seasonings and basil. Stir in the heavy cream and freshly grated Parmesan cheese. Continue stirring until the cheese has melted and the soup is creamy. Taste and adjust the salt and pepper as needed. Add in your lemon juice.
While the soup is finishing, prepare your grilled cheese sandwiches. Butter the outside of your bread and fill with your favorite melting cheese. Cook in a skillet over medium-low heat for 3 to 4 minutes per side, until golden brown and crisp and the cheese is melted.
Ladle the tomato basil soup into bowls and garnish with fresh basil and an extra sprinkle of Parmesan. Serve hot alongside the grilled cheese for dipping.
