This is so versatile! I've made it as just the stew with some crispy garlic bread, I've also braised chicken, and fish in it. If I do chicken I prefer bone-in breast or thighs, thighs add great flavor! If I do fish I go with something a bit dense that will hold up and not just flake away into the broth. Something like monkfish, swordfish, or even just a few shrimp is perfect.
In a medium sized soup pot put oil and onion over low heat and let the onions get nice and translucent.
If adding chicken do so now, sprinkle it with some salt and pepper and put it in the pot skin side down and brown it up for a few minutes. If adding fish that step comes later to adjust for cooking times.
After the chicken has cooked for about 5 minutes add the tomato puree.
Let the puree simmer for about 10 minutes, it should thicken up at this point.
Add the potatoes and carrots and cook for about 5 minutes then add the rest of the veggies.
If you're adding fish, now would be the time to do this. Sprinkle with salt and pepper and lay on top of veggies(soup should be pretty dense by now.) Let the stew simmer for about 10 minutes. Check to make sure the fish/chicken is cooked through and the veggies are done, too.