@Tim35 - That is exactly it. An egg would have the “equivalent” of 3.5g of carbs and you dose based on your I:C ratio for the day. If I ate a 60g carb breakfast and had one egg, the 3.5g of carb would just be noise and probably within my carb counting error range. If I had 4 eggs for breakfast (14g) and no carbs - then around 2.5 hr later, my CGM would start to slowly go up by about 60 (3.5 mmol/l).
As you noticed, there is only 0.5g carb equivalent in fat in one egg, so I often just ignore the fat and focus on the protein.
For protein and fat, I always use an extended bolus. 0% up front and 100% extended.
I aim to deliver about 1.25 U/hr to cover the protein - but round to the nearest 1/2 hour. So for 1 egg (based on my I:C ratio of 7), I would deliver over 0.5 h and for 4 eggs either 1.5 hours or 2 hours depending on my blood sugar at the time. If BG is lower, I would use 2 hr / higher I would use 1 hr.
So where does the 1.25 U/hr come from? - I started with what @Terry4 used and adjusted it a bit 
- Since it works for me, I have never bothered to look into it further. I suspect if you wanted to go there, the number would be based on the rate at which your body converts protein (ok - amino acids) into glucose. It is pretty easy to measure your carb absorption rate (eat some glucose and see how long it impacts your glucose for). I would assume one could come up with a “protein absorption rate” (a very unscientific name but you get the idea) based on a bunch of variables.
Protein is alleged by some to have effect on blood glucose in the 3-6 hour range (depending on where you look on the internet the numbers are different). For me, I start to see an effect at the 2-2.5 hour mark if I eat protein only (ok protein and fat - like cheese) when I am flat lining. The 1.25U/hr thing usually gets enough insulin in slowly enough to match my “protein absorption rate.”
There is a old TAG group here that may have more info: