When I make a "cream of" soup, I usually feature just one vegetable. But I always add some aromatics—garlic, shallots, onions, leeks—to make the flavor more complex.
The fat used to sauté the aromatics also adds flavor —
Butter adds richness, bacon fat a wonderful smoky flavor, and olive oil a light, fruity note.
The thickener is added along with the liquid —
For every 2 pounds of featured vegetable, I add about 6 cups of liquid. Most puréed vegetable soups call for broth, but you can use milk or water, or a combination. It's easier to thin a soup once it has been puréed than to thicken it, so err on the side of less liquid rather than more. The potato or rice goes right into the pot with the simmering liquid.
Begin by sautéing some aromatic vegetables over medium heat until soft. If you want the flavor of a robust, resinous herb like thyme or rosemary, add it now. Then add liquid and simmer.
Add the thickener—1/2 cup raw rice or a sliced raw potato. These starchy ingredients swell and give off starch during cooking. When the soup is puréed, they'll make it look and feel creamy.
When to add the featured vegetable depends on how long it takes to cook —
Long-cooking vegetables like carrots or turnips should be added at the same time as the starch, but quick-cooking vegetables like spinach and sorrel should be added when the starch is almost cooked (see Vegetable timing chart). This isn't an exact science, so don't worry if the starch needs a few extra minutes. Just be sure that you're able to smash the potato slices easily against the side of the pot and that the rice is plump and tender; otherwise, the purée may be grainy.