How do you treat a big toe which has thick callous that has now cracked and causing discomfort?

Very carefully!
It is important to pear down the thick callous tissue in order to heal the cracks which have occurred. If the toe is too uncomfortable, this may be a slow process.
Soaking the foot and gently filing the callous could be effective and the least uncomfortable.
Follow with a cream like Attractain, will also soften the callous and heal the cracks.
Remember callous occurs due to pressure so check the footwear and make any appropriate changes.