I scrubbed (but didn't peel - I generally don't peel) the carrots and the potatoes, and top-and-tailed the carrots. These I cut into rough 2cm cubes. I chopped the peeled onion quite fine, and crushed the garlic. All of them went into my ordinary large saucepan, just covered with cold water. I brought them to the boil, then turned down the heat to a gentle simmer and skimmed off the small quantity of scum that had formed on the surface. You only really need to skim if you're making a clear soup, but it's got to be a habit with me, so I did it anyway.
When the vegetables were tender but not soft, I strained out a large cupful of them and set them to one side. Meanwhile I'd been defrosting a large skinned and boned breast portion of chicken - about 350g. I cut that into 1cm strips, and then again into cubes, which I added to the pan to poach gently, making sure there was just enough water to cover everything. At that point I also added two one-pint stock cubes: one chicken stock, one vegetable. Of course, if you use your own stock, then you'd have cooked the vegetables in the stock rather than using water... Initial seasoning was a healthily large grind of black pepper, a teaspoon of dried herbs, and about a half inch of blade mace chopped into tiny pieces (I find that mace somehow just won't disintegrate in a mortar and pestle, so I chop it).
That simmered until the chicken was cooked through, and the vegetables were soft. I took out some of the chicken cubes and added them to the vegetables I'd set aside earlier. Then it was time to blend, so I let the pan cool somewhat, and then blended the contents until it was just on the slightly granular side of smooth. Then I put in the reserved vegetables and chicken, and finished off with a 200ml carton of single cream. If there'd been any need to adjust the seasoning, I'd have done so at that point, but as it happened there wasn't.
Result: somewhat over three pints of absolutely delicious soup.