Peel and finely chop the carrots and onions, chop the celery sticks and break the cauliflower into florets.
Melt the butter in a large heavy-bottomed saucepan, add the vegetables and stir to coat. Cook the vegetables over a low heat, stirring occasionally, until they start to soften, about 10 minutes.
Add the stock, season with salt and pepper and bring to the boil. Reduce the heat and simmer for 30 minutes.
Strain the vegetables, reserving the liquid. Purée the vegetables and return to a clean saucepan. Stir in the reserved cooking liquid and then stir in the yogurt. Reheat gently but do not let it boil.
* If there is no homemade stock to hand, use a good commercial stock. I always check the ingredients of commercial stock as they can have a lot of sodium in them as well as other additives which I would rather not use – sort of defeats the point of making home-made soup. In the U.K. I tended to go for the organic stock cubes and in Canada I have found 'Better Than Bouillon' to be really good.