Other kugelhopf/gugelhupf recipes I've seen call for only 2 eggs - what's the function of the eggs in this recipe? Why does it call for more? Just...

I'd give one of my cats for an Edit function! But I trust you get the gist of this typo-infected answer, Anneliese.

I've not made Tom's Kuglehopf, and I can't speak for him. But in Peter Reinhart was my Breads chef-instructor in culinary school, and his kugelhopf from his book Crust & Crumb was our gold standard. While Chef Peter's mixing method differs a bit from Tom's, Chef Peter's actually calls for 1 more egg than Tom's. In both cases, the function of the egg is to both enrich the dough (the yolks) and strengthen it (the whites). They're also going to make the dough much more sticky and a bit tricky to handle, which may be why some recipes call for fewer eggs - to that the dough isn't as much of a challenge. That said, I'd definitely suggest following Tom's recipe to a, no pun intended, T, as I suspect you will love the result much more than one calling for fewer eggs.