The secret to binding burgers without eggs is to use an ingredient that will both absorb extra liquid and become somewhat sticky to hold things together. There are several options for this. I like using either ground flax or ground chia the best. Both of these can be used at about 1 tablespoon per 1 egg the recipe calls for. Using ground seeds will help reduce potential grittiness you may notice, and help them absorb liquid better. Most people combine the seeds with water before adding them to the burgers, making a "flax egg" or "chia egg." But I find I get better results by sprinkling the dry ground seeds directly into the burger mixture, and allowing the them to absorb extra liquid from the mix to bind it.