In a bowl combine the cooked rice, 1/2 cup breadcrumbs, eggs, salt, sriracha and ham. Mix it all thoroughly and knead it a bit to bring it together. Take a small handful of the mixture and place a cube of the pepper jack in the middle of it. Form the mixture into a tight ball surrounding the pepper jack. With the size that I made mine, I got 10 croquettes out of the mixture but this could vary depending on the size you make them. Adjust the amount of pepper jack cubes you cut up based on how many croquettes you yield. Roll each of the croquettes in the additional breadcrumbs to thoroughly coat them and transfer them to a platter when they are done.