My wife and I both enjoyed this recipe a lot, though my son thought they were marginal. Next time, I may want to try these with bleu cheese. The Longbranch in Leshara, Nebraska made burgers with the same concept, placing cheddar or American cheese with grilled onions in the middle of the burgers.
ADDENDUM: It took me awhile, but I finally tried these with bleu cheese, and we like them even better that way, probably because the bleu cheese has a stronger flavor. I made sure to place a large charge of bleu cheese smack dab in the middle of the burger, in addition to mixing bleu cheese with all of the hamburger. I added a few extra splashes of Worcestershire sauce too. Remember to find that fine line between mixing the ingredients enough so the meat stays together and the ingredients are evenly distributed, but not so much that the burgers become dry because the meat is too compressed. Keeping the hamburger somewhat loose is the secret to juicy burgers.