You can just flat out share for no additional charge. Or you can pay the split plate fee (maybe around $8?) to have it plated separately with each individual getting their own soup and side.
I think it's also a little different if it's kids or adults. Just my two cents but I think at a dining place like BB it would be more appropriate for adults to have the plate split than to just order one meal and eat off one plate. Don't get me wrong, we share food at many places in Disneyland because I agree the portions are large, I just wouldn't do it at a "fine" dining like BB.
Split plate is $12 at BB. My daughter and I split a Monte Cristo on Sunday 9/18. She really likes their bread and Gumbo. We never make it far with the Monte Cristo. Love the waterside view.