I haven't read Neanderthin so I don't understand the theory of it although I gather it is a low carb program. I do Atkins. Maybe you could read the DANDR and see if that gives you some insight.
The meal you described doesn't sound very appetizing to me. I need to have something satiating. I might suggest a nice big omelette.
Drop some butter into a frying pan, add a good amount of red peppers diced up, a good lot of regular canned mushrooms (tasty, low in carbs, filling, healthy) maybe a little zucchini or yellow squash in thin slices. Fry it up for a couple of minutes and add a couple of scrambled eggs beat in with a small amount of cream. A half tblespoon of Sour Cream nakes a nice condiment and then salt & pepper.
This sort of meal usually leaves me with feeling satisfied.
Again, I can't speak for Neanderthin. Only my success and satisfaction with Atkins.