Start by stripping your vegetable
In this case, I peeled the carrots and trimmed off the ends.
Chop the vegetables into small, even pieces
Choose your cooking method
I prefer boiling whenever possible, because it's quick and kills two birds with one stone: if you flavor the cooking liquid, you can later use it for the blending.
My favorite formula is one part cream to three parts chicken stock. I love the balance of flavor and creaminess it gives.
Add enough liquid
If baking or sauteeing instead, try not to use excessive amounts of fat, which could make for an oily emulsion if you plan to add liquid or cream later.
Season as you wish
Here I brought the carrots to a simmer and cooked them fully, until a fork passed through with no resistance.
Drain the vegetables, reserving the cooking liquid
Start ladling the warm cooking liquid into the blender. (If you used water here or plain stock, have some extra liquid and heavy cream warm on the stove for this step.) Add enough cream and liquid to cover the vegetables by about half. You will most likely need more, but it’s easier to add liquid than take it away.
If you have a Vita Prep or other high-powered blender, yay for you—whip that bad boy out, cover it carefully, and turn the speed from low to high as the puree breaks down.
Test it by spooning a bit onto a plate. I like mine thin enough to run a bit, but not so thin that it doesn’t hold shape—sort of like a melty, soft-serve ice cream.
If you were working with a tough or fibrous veggie, or one with skins or shells like tomatoes or peas, this would be the point at which to run the puree through a medium-mesh sieve to smooth.
Adjust seasonings. Stir in any additional cream or liquid. Garnish, Serve!