Herb infused oil - what went wrong
Hmmm, funny you should ask that. Just now I am experimenting with using oil and other edible stuff to extract various chemical compounds from herbs without waste of those compounds. Grit or any identifiable vegetable matter is definitely a negative. It is very much the same thing you are talking about because flavor compounds vary in particle size and solubility.

So far, this product has shown great promise in my experimentation:


They work like cheesecloth, but the filter has holes measured in microns (25 - 220) instead of millimeters. You can wring the heck out of them, wash and reuse. They are constructed kind of like paper grocery bags, each about 1 gallon or 4 liters capacity. The bottom panel is a mesh filter.

It may be an odd off-label use because these things are actually for making hashish, but I saw their culinary potential when I first saw them at a fair. I'm using them now and they really work well to keep infused oils made with ground dried herbs grit-free. You can't wring them too hard, they can handle it.

If a clear, grit-free infused vinaigrette with finely ground dried herbs or food-processed/blended fresh herbs was my goal, I'd definitely give these a shot. Think of them like adjustable, reusable coffee filters.