Mix green chiles, onion, mustard, butter, and poppy seeds together in a bowl; spread about 1 tablespoon onto each cut side of each hamburger bun. Layer two pieces of ham around each slice of Swiss cheese and place onto the bottom halves of the buns, sandwiching the meat and cheese with the top halves.
Wrap each sandwich in aluminum foil.
Bake sandwiches until the cheese is melted, 6 to 10 minutes.
