Leftovers saving noodle soup

I have a soup problem. I was raised with an idea that soup is something you are cooking in a huge pot and then eating the whole week (ok maybe not 7 days in a row but at least 3-4). But nearly all of them taste the best when just made and this causes all the problems. There are three of them which I’m trying to address while cooking for my family of two:

1. Utilising as many leftover veggies etc as possible

2. Creating as less leftovers as possible

If the first point seems fairly clear, the second one often causes troubles. Even though in my family of two both of us are soup lovers, quite often the last portion after staying in a fridge for a week (or even two) goes to the wastes. I’m not talking about bits and pieces of ingredients like e.g. tiny knob of already peeled ginger, quarter of a carrot, half of a