Once you have the basic ingredients it will also let you throw in a few random vegetables without having a major strop. So for the basics.
There is no need to sweat the vegetables as you will be cooking this soup slowly and the flavours will have time to develop.
Simply put a pan of cold water on the hob and add to it as you go along. The amount of water varies according to the number of people that you cook for. Let's say about 2pts for 4 people.
To this add
1 medium onion,
2 sticks of celery
1 bay leaf
1 small potato approx 120g. Don't get too precious as it can be slightly bigger or smaller.
1 large vine ripened tomato or failing this about 1/3rd of a tin of tomatoes.
A few stalks of flat leaf parsley
I don't even bother to chop the veg up finely. You will soon see why.
Bring slowly to the boil and allow to simmer gently for about 1 hour. This is no hardship as there will be a lovely smell in the kitchen. Now use a potato masher and give the veg in the pan a bit of a bash. Don't make them too fine as you still want to identify them. They should just be broken up.
You can now add any variations that you have. I like to add a handful each of:
cauliflower florets which have been cut small
peas, frozen are fine but fresh are better
finely chopped dark cabbage
precooked borlotti beans.
Do not add swede, parsnips or turnips as they will not make a good soup.
Allow the soup to simmer until these vegetables are cooked and then season to taste with salt and pepper and a stock cube if you have one.
Add a small handful of small pasta per person and cook until soft.
Serve with a drizzling of extra virgin olive oil and lots of freshly grated Parmesan cheese.