In a medium pot over med-hi heat, add Olive oil and onions and sauté until translucent 1-2 minues. If you are using carrots for sweetness, add them at this time as well.
add garlic (minced) and stir,
Add canned tomatoes (crush or mash them as you put them in-I crush them with my hands), passata and chicken stock and stir. Add Sugar, if using
Add salt and pepper and let simmer for about 15 minutes, taste and adjust salt and pepper if needed
Add Basil, grated fresh parmesan (and 1" piece of parmesan rind) and cream. Stir to combine
Process with a hand immersion blender in the pot, or alternatively in a blender
If using a blender, fill blender up halfway and hold the lid down with a towel to prevent the lid from coming off due to the heat.
Puree in batches until its all done. Let simmer for 5 more minutes to let flavors combine.
Just before serving add additional parmesan or basil to taste.
Taste and adjust, you can't really mess this up. if its too tangy, add
another tsp of sugar
remove the parmesan rind, if you used one.