Pre-heat grill to medium heat. Mix the mayo and mustard together and set aside.
Add beef, pork, zest, and seasoning to a medium bowl. Mix by hand until everything is evenly mixed.
Pat four burgers. Place burgers on the grill and grill 5 minutes per side. Once burger temperature has reached 150°F. Place ham and cheese on the burger. Allow the cheese to melt and burger to reach 160°F.
Remove burgers from grill. Spread the mayo/mustard sauce evenly on all burger buns. Add pickles, and place burgers on the buns.