Picked up this one during my days in Xalapa, Veracruzana in ’00. 

Cut two onions, three potatoes (onions and potatoes: fist-sized) and 10-14 large carrots into big chunks. 
Drop them in a pot with water just below the top of the vegetables.  The
onions will reduce into liquid while boiling, so the space they take up is
temporary.  Salt the water; I don’t know, a teaspoon or two.  Cover
and boil for thirty or forty minutes until everything is soft.  The smaller
you cut everything, the faster this part will go, but I don’t have any patience
for working the vegetables when I know they’re going to end up blended.

When the vegetables have softened (if in doubt, remove a carrot, check it),
cut the ends off of a single green chile (alternative: a jalapeno) and drop it
in the boiling mix.  Cover the pot again and give it another 7-10 minutes. 
Basically, this just softens the pepper.  You could go to all the trouble
of preparing the chile in other, more complicated ways, but basically I want it
to soften so I can remove it to cool, slice it lengthwise, pull out the seeds,
and have it ready to join up smoothly with everything else in the blender
(that’s next).

When the vegetables are soft, you should transfer them to a holding bowl or
alt. pot for blending.  I transfer them so I can easily empty the blended
soup into the original pot.  Next, use a ladle to fill the blender between
2/3 and 3/4 with the boiled vegetables and the hot liquid they cooked in. Then
I add 2% milk to fill the blender just a bit more; somewhere close to 7/8 full. 
Then blend.  I’d say it works best when you have enough liquid to
incorporate the vegetables.  You want them to be smooth (unless you prefer
chunks in the soup; if that’s the case, best of luck).  Blend and blend. 
And then pour the blend-pitcher into the original pot.  Repeat.  Be
sure to work in the green chile.  It adds the kick. 

Eventually you’ll have a steamy concoction of more or less creamy vegetable
soup, carrot soup in this example.  Next I  add about three or four
teaspoons of dry chicken or vegetable bullion, then let it simmer for another
thirty minutes.  Sure, extra pepper and salt are fine additions, too. 
And if you decide to sub out the carrots and use squash instead, consider adding
ginger (for a nice cream of gingery squash soup).  Actually, you can
replace the carrots with just about anything–zucchini, asparagus, etc. 
And, if you’re into richer dairy (as in something creamier), leave out the
potatoes and use a heavier cream.  I’m not so fond of the dairy products,
so I include the potatoes for thickening and use a bit of milk. 

That’s all.  I know it’s not the kind of recipe circulated by
cooking-types inclined to strict measures.  But it’s relatively light,
uncomplicated and just spicy enough to ward off the common cold or offset a
drafty window with some lasting warmth (yes, and also gentle on grad student
budgets).  Enjoy it with some quick-nuked quesadillas (tortillas, cheese(s)
of choice, etc.) or something more elaborate if you’re planning a fancier meal. 
Also keep a lime on hand in case anyone finds the soup too spicy.  A
squeeze of fresh lime juice will cut the spice-heat by a bit.

If you’re unimpressed, here’s last December’s solstice recipe.