Put the lamb mince, seasoning, onion and mustard into a large bowl. Mix together thoroughly.
Divide the mixture into four and shape into burgers. Line the grill pan with foil and place the burgers under a pre-heated grill and cook for about 12 minutes until golden and cooked through.
Make the Welsh Rarebit. Mix together the mustard, cheese and beer.
During the last 1-2 minutes of cooking place the rarebit in a mound on top of the burgers and allow to melt and ooze over the burger. Collect any juices in the bottom of the grill pan and spoon over the burgers. Serve with chunky fries and seasonal salad or slaw.