I had never heard of this, until I did an internet search on a hunch, & therefore doubt many other people on this site have heard of it either. I did the search since I have read of the shortcomings of the glycemic index, glycemic load model – essentially they only look at glucose so the effects of artificial sweeteners, fructose, fats, etc, are not considered.
To improve on the GI/GL model, the Food Insulin Index (FII) measures the bodies insulin response to ingesting food versus simply looking at blood glucose levels (for example, foods containing high fructose levels do not cause Blood sugar spikes but can cause insulin spikes). Helps explain why some foods, previously considered good for diabetics or weight loss, may not fit the “bill”.
Anyhow, worth a read.
Following articles review some recent research, or provide more info. https://optimisingnutrition.com/2015/03/30/food_insulin_index/
http://www.mendosa.com/blog/?p=3624

In general, I agree that the GI is a good tool & simplest to use.
Second link provides some interesting differences. Low fat dairy products tend to be double, or more, on the FII vs GI. Examples given are low fat strawberry yogurt (FII 84, GI 21): low fat cottage cheese (FII 52, GI 10), etc.
What isn’t discussed in what I saw is whether or not those products incorporate any non-sugar sweeteners (agave, stevia, sucralose, etc). Often some sort of sweetener is added to low fat products to offset lack of fat/make them “palatable” . I presume non-sugar sweeteners since the GI is low.
Some studies (according to Dr Fung & others) show that while non-sugar sweeteners may be low on GI, the body interprets them as sugar & secretes insulin (“sugar” receptors can’t tell the difference). The author in this case states it is dairy protein causing the effect, but only list low fat dairy products as having the wide differences!

Something to consider, but think more research is likely needed.