Try carbon steel. Seasoned, it's a great nonstick pan.

why steel over cast iron? Im guessing more ghee/beef tallow wouldn't help?

Scrub up the cast iron with vinegar. Make sure to rinse all vinegar out. Then just start using it. I don't think seasoning is necessary, this will happen as you cook in it with plenty of oil. Make sure to use a spatula with a flat edge to evenly wear the pan down to 'glass'

Do you have a brand you recommend for carbon steel? I love cast iron, but don't want a big pan that weighs 80lbs 😁

I like De Buyer pans, but I'm sure there are a number of decent brands out there though.

My tip is heat the pan with the fat (enough) until you can see the fat being hot and it makes waves (moves due to heat) then add the eggs already mixed before for omelette or scrambled eggs. Then once you put it in the pan let the mix sit for a bit and finally mix and cook through. Requires practice but worth it. No non stick pans is right. Bad chemicals in them.