Larry, good to see you.
Any of these sauces can be changed to more of condensed mushroom soup white sauce.
Starting with this one, instead of dairy/butter, moving to plant fats.
It uses cashews for the fat and mouth feel.
Skip the onions, or not.
https://sweetsimplevegan.com/2018/01/healthy-cream-of-mushroom-soup/
Then if you want to move towards a different plant fat, then use this type of recipe.
It uses tahini, a seed fat instead of cashews, and skip the nutritional yeast. add mushrooms but it is orange in color. You can taste the red peppers and it is a nice flavor for nacho-ish flavor.
https://detoxinista.com/red-pepper-cheese-dip-vegan/
Then if you want to move towards a no oil sauce (we are for heart reasons), try this one.
It uses no fat, based on potatoes, the texture is smooth (make it in a food processor or strong strong blender). You can make it white by replacing the carrots with cooked onions and more potato. Add mushrooms and skip the nutritional yeast if you don't want a cheesy flavor. It is by far our favorite and we used it on pizza today in it's original form.
https://simpleveganblog.com/fat-free-vegan-cheese-sauce/
Then if you continue no oil, you can make this one.
It has a base of cauliflower, add mushrooms, skip the paprika, turmeric, and nutritional yeast to make it white and non-cheesy in flavor, thicken with corn starch or potato starch. (There are others, that have a stringy type texture (like mozzarella) using tapioca flour--I've had good luck with that.)
https://blog.fatfreevegan.com/2013/05/cheesy-cauliflower-sauce.html
This last one is great too no oil. Made with red peppers but thickened with oats pulsed in a food processor, or oat flour, and corn starch, but orange nacho-y and cheesy. You can make it in a vitamix or for me, a regular blender, then heat to thicken on the stove.
https://www.copymethat.com/r/7jwomBD/jills-game-changer-cheese-sauce/
To get the mouth feel of oil without oil, you can put a teaspoon of cornstarch in water, whisk it and cook until clear, then use that. Or I've found that xanthan gum, a quarter teaspoon to a 1/2 cup of broth or water, mixed cold, gives that same oil mouth feel.
I've tried most of these working through having no oil ways to serve different whole food plant based foods. My hubs is thrilled with that potato cheese sauce, eats it on ww macaroni. I've used it on toast with asparagus for a lunch.
I learned a lot from an indian woman who was teaching me how to get more 'sauce' in my curries, she cooks up some of the softer vegetables first with the spices, then kills them with an immersion blender, then continues on by adding the larger vegetable pieces and cooking them until tender crisp. The sauce taught me everything I was wondering about.