Soup of the Day, a stock item

As the Chef in a moderately-sized hotel in Silicon Valley, it's part of my daily routine to prepare a Soup of the Day and a Daily Special. Soups are one of my favorite things to make and fortunately as a result of years of practice I make excellent soups. (When I worked in the cavernous kitchens of Pac-Bell I was known as the "Soup King", making two soups a day in 50 gallon steam kettles). The requirements are more modest these days, but I prepare all my soups in more or less the same way. I like to make my own stock, though I'm not averse to enhancing it with commercial soup bases.

Chicken Stock: Obviously it's part of my job to save the hotel owners money, so I look to be as economical as I can. So let's say I decide to make Moroccan Chicken or Chicken Cacciatore as the Daily Special. I always have whole chickens on hand, the least expensive and most versatile way to buy chicken. When I cut up my chicken for the special, I remove the backbone and the wingtips, parts that probably aren't going to get eaten anyway, at least not in this part of the world. Although if you watch "Bizarre Foods with Andrew Zimmern" on the Travel Channel you know that someone somewhere is eating every single part of a chicken, except perhaps the feathers!
Then I take those removed parts and roast them in the oven because I would much rather have a stock with the color and flavor of roast chicken than one made from the raw bird. I throw those parts in a pot with the peelings and scraps from onions, celery and carrots that I've saved over the previous few days, cover with cold water because cold water gives a less cloudy stock, bring to a boil and let simmer for at least a couple of hours, longer if I can, adding water as needed.
Then I discard the solids, and I have a chicken stock with color and flavor that didn't cost anything to make because I used the scraps left from other dishes.

I almost always start my soup with a "mire poix", another one of those unnecessary French terms that plague the food business. It simply meams a mixture of diced onions, carrot and celery, the "aromatic" vegetables, in the ratio of 2 parts onion to 1 part carrot and 1 part celery.
I put my heavy soup pot on low heat with a splash of vegetable oil, and when I see that shimmery web in the bottom that tells me the oil is hot, I toss in my mire poix and let it sautee slowly, stirring from time to time, so that it develops color without burning (if you're planning to puree the soup, a little burning won't be noticed. Just tell yourself that you never burn anything, you just carmelise in different degrees) .
Today I made Cream of Mushroom, so the next thing to go in was a couple of cupfuls of sliced mushrooms. I added a couple of tablespoons of beef base to the mushrooms to bring out maximum flavor and let them cook down until they released all their moisture. Then I added chicken stock to cover and a little more, turned up the heat until it came to a boil and then let the whole thing simmer for a half hour or so until the vegetables were soft.
I took the pot off the heat and pureed the contents with an immersion blender. Mine's a household model, not especially expensive, although the largest commercials ones cost several hundred. Once I had a smooth puree I put the pot back on the stove, added a couple more cups of sliced mushrooms (hint: an egg slicer makes a great mushroom slicer and won't cut your fingers. works for strawberries, too). After those mushrooms have cooked down a little, I turned off the heat, added cold milk (2% is fine) to the pot, approximately equal to half the liquid that was already in the pot and add my roux. Roux!? Who!? (pronounced "roo", another gallicism).
Roux is simply a mixture of liquid fat and flour. It can be melted butter or margarine, chicken fat (liquid gold), beef fat, bacon grease, or in the case of a Cajun roux, very hot oil. The fat and the flour are combined and cooked over low heat to get rid of the raw flour taste. Then it's ready to use. It is simply a thickening agent. But if you add roux to a boiling liquid, the clumps of roux will solidify and cook before they can disperse and do their job, leaving you with little roux dumplings in your soup. That's why I add the cold milk and turn off the heat, to bring down the temperature to a safe point to add the roux. Then it can be whisked in easily.
Once the roux is well dissolved, I turned the heat back up to medium and let it do its work, at least another 15 minutes or more. If you decide your soup is not thick enough and you need to add more roux you will have to let the soup cool down again (adding a few ice cubes will usually do the job quickly).
Once the soup is nicely thickened, smoothly pourable, not thick enough to lay bricks, turn off the heat, let cool a little, then season with salt and pepper. You will get a better sense of taste if you don't burn your tongue as soon as you put the soup in your mouth. I generally prefer the milder taste of white pepper to black for most soups and for white meats. I will add a small amount of heavy cream at the end for a touch of richness.