You're definitely asking in the right spot. I just don't know anything about broody cages. Does this mean you're looking to make a cage in which your broody hen can sit on her eggs or do you mean a "brooder" cage where small chicks are kept?
I haven't dealt with that one yet! I thought that when it happens, I'll use a large dog crate with a box inside for the hen and panels of hardware cloth on the outside. Sorry I couldn't be of more help. Hopefully, someone with more experience than I in this area will chime in.
I've used large cardboard boxes before, lots of air holes around the box. Big enough she has room for water and feed and to get up to poo. I cut the bottoms out and add pine shavings. Just put a large window screen for the top. Do you know someone with an old large wire dog crate? Those work well.
There's is a broody pen the young man is working on in the poster, can be made from scrap wood, place a clutch of eggs and a hen inside, it forces them to sit on the eggs till hatched, feed and water daily. Make as many cages as you want for multiple hatches/birds/sizes.