I am looking cook a breakfast goulash to serve 30 people. It seems like breakfast goulash is usually done in a large frying pan (see this recipe).
The quantity I am aiming to make, however, will not fit in any frying pan, so I am wondering if I can carry this out in a very large pot. However, will 30-40 eggs properly cook in a pot, and are there any nuances I should be aware of?
You are going to have trouble scaling that recipe up to that size, due to the limited heat output of a home type burner element or electrical element. They can only have sufficient power to brown so many hash browns, or cook so many eggs at once. Furthermore, most home cooks don't have a pan with sufficient surface area to manage that quantity of ingredient in one go--there is a reason that restaurants and institutions use large flat griddles for the purpose, not large pots.
Instead, I recommend that you look to a class of similar breakfast casserole dishes that you can bake. This will offer you better scalability, and less risk of scorching or burning, and almost certainly be less work.
It is much easier to put two or three casseroles in the oven than to manage a stove top dish at that scale.
You can scramble your eggs in batches and keep them warm in the oven at around 60ºC. This way, when you're going to serve the scrambled eggs, they're going to be warm. At that temperature, the eggs are going to be safe and won't overcook.
Check-out these charts about food-safety, there's one for eggs.
