To peel and seed them, fill a saucepan 3/4 full of water and bring to a boil. Using a sharp knife, score an X in the blossom end of each tomato. In batches, without crowding, immerse the tomatoes in the boiling water and leave for 15-30 seconds, or until the skins just begin to wrinkle. Remove from the pan with a slotted spoon, let cool slightly, then peel away the skins. Cut in half crosswise and squeeze.
gently to dislodge the seeds.
In a large soup pot over medium heat, warm the oil. Add the onion and saute, stirring frequently, until softened, 5-7 minutes. Add the garlic and cook until softened but not browned, about 30 seconds.
Add the tomatoes and stock, raise the heat to high, and bring to a boil. Reduce the heat to medium-low, cover, and cool until the tomatoes are softened, about 30 minutes. Remove from the heat.
In a blender or food processor, puree the soup in batches, leaving a little bit of texture if desired, and return the soup to the pot. Alternatively, process with a hand held blender in the pot until the desired consistency is reached. Return the soup to medium heat and reheat gently. Add the chopped basil and season to taste with salt and pepper.
Sprinkle with a spoonful of Parmesan cheese. Enjoy!