Are you trying to make a sauce or gravy? Here's how I do it:

-cook whatever meat in a pan, remove meat, leave cooking eye on
-add a tiny bit of water (usually less than an 8th of a cup is plenty) which should come to a boil in a few seconds
-add enough heavy whipping cream to create a gravy-ish consistency (usually 1/4th cup or less is plenty)
-add a little butter if you need to thicken it
-add pepper liberally and a bit of salt if you need to

It's not as good as regular starch gravy of course but it ain't bad at all. I come from a long line of fine Southern cooks and no one has complained about eating my Argo-free "gravy" yet.

Obviously, whip with a whip or fork the entire time!

I don't use any of that stuff. It causes me to stall. I don't trust it.

Duxelles can be used to thicken soups and sauces. Here's the definition. I've also made it by simply whirring mushrooms in my tine food processor.

I have used something called Gar Gum, I'm not sure if that is the right spelling. My only complaint is that when you put it in stuff you really have to mix (like a mad women). I recently used it in some soup and had lumps, I tried to put some in a glass with water, like when I used cornstarch, but it thickened the water so fast and so thick that I could turn it upside down and nothing moved it looked like clear jello. Anyway, it works great, you just have to practice. I found this stuff at a health food store and when I was there they als recommended something, which I don't remember the name, but it was dried seaweed.