No recipe used, just my intuition. This is my 2nd iteration. I cook 8-12 days worth of food at one time. Today I made my typical bake-everything at once deal, with chicken tenders over a bed of onion slices and covered in the lemon garlic spice pictured. I had the idea of turning the onions into a purée in a food processor and turn this into a sauce with the remaining lemon garlic flavored chicken stock. To this I added sriracha, Worcestershire (ancient roman garum like fish sauce), brown sugar (an American is gonna be American), and I used cornstarch to thicken the sauce considerably.
My biggest complaint is presentation. It is not a pretty sauce. I may try mixing it with some mayo at some point to use more like a condiment.
The last iteration was not thickened with cornstarch and it never separated out or lost texture. I'm open to ideas and suggestions for improving the taste or presentation value.
Overall, this sauce is kinda like a teriyaki sauce or something. I'm not sure what to compare it to really.
The following image was from 15 days ago and shows the chicken over onions more like how I cook it in a dish although still not the actual dish I cooked it in. Also, this image shows my first lactic fermentation attempt just after I started. You can make out the jar in the background of this main post image. It is coming along fine, a bit slow, but still bubbling along and getting burped daily.
You just stumbled onto one of the great hacks of Indian cooking: Onion Masala base. https://myheartbeets.com/indian-onion-masala/ try the butter paneer in this series - so easy, so good.
Keep in mind, those Ninja things have whacky blades, but they differ. One is a "processor" blade, and another is a "blender" blade. I'd venture a guess this is just processed.
Anyway, to your point: the secret to sauces is sifting and filtering. It's kind of a quick 3 step process:
marinate
heat (heating is somewhat optional in some cases)
blend
sift/filter
If you want a smoother sauce like you'd find in a bottled product, you have a few different ways to go to finish:
You might want to try Xanthan Gum as a thickener. It is flavorless, does not discolor or cloud sauces, and is temperature and pH stable. It does not need to be heated to work.
I've actually made a pretty similar gravy (I like it with meat loaf). One thing I've done is, rather than thickening with corn starch, try a roux made with beef tallow as the fat.