Preheat the oven to 275 degrees.  Line a small baking sheet with parchment paper or a Silpat mat.  Set aside.

In a large skillet over medium heat, melt the butter.  Saute the onion and garlic in the butter until the onion is translucent, but have not started to turn golden.

Meanwhile, roughly chop the ham.

Once the onion is translucent, add the ham to the skillet and begin to separate the pieces as you toss and mix it with the onion and garlic.  Cook for 5 minutes, breaking up any lumps of meat.

Meanwhile, in a medium bowl, stir together the ketchup, relish, vinegar, water,brown sugar, yellow mustard, and Worchestershire sauce.  

Pour the sauce over the ham and stir well to completely combine.  Allow the mixture to simmer, stirring often to keep the mixture from sticking, until the sauce has thickened and reduced – about 20-30 minutes.

Spread both sides of each Kaiser roll with butter.  Place on the prepared baking sheet and bake in the preheated oven for 5-7 minutes until lightly toasted. 

Assemble the sandwich by scooping the ham barbecue mixture onto the bottom of each roll.  Top with the toasted top and serve hot.