I put my aquadulce seeds into root trainers, outside in racks at home, in january this year and have got amazingly good strong plants to put out in march.
Rootrainers are a good idea but I can't get my head around why they charge so much for something so fragile.
There are various alternatives but the easiest for large seeds is to make up a roll - I have done this many times with small oca or to make seed potatoes go further by using smaller bits - it works a treat but I didn't think of using it for broad beans until your post - they are about the same size as some of the oca or spud bits I've used in the past.
Basically it's the same as the roll of cuttings method - you take a sheet of plastic a metre or so long and wide enough to give twice the depth that you want for your "Rolltrainer" - fold it widthways and make a line of holes down the closed edge - I use scissors and make little snips.
You open it out and put a layer of compost to cover one half between the holes and the edge - about 2-4cm deep - put your seeds or tubers in at the right distance from the edge and at least 10cm apart, fold it over and roll it up.
It's nice if you can find a big plastic pot that the roll will fit in. but otherwise it needs to be taped or tied up. Brown sticky packing tape is surprisingly waterproof for a whole season once it is stuck firmly to clean dry plastic (or itself).
You just unroll when you want the plants, lift them out and transplant.
It's well worth including straight sticks (prunings) as you roll it up to squash the sides together at intervals to make pockets that will tend to stop the roots getting intertwined.
The more alternatives we can find the more pressure on rootrainers to use better materials - like the throwaway trays my sausages come in - which are about 10x more durable than what they charge £££ for...
Cheers.