Preheat the oven to 350 F (176 C). Use butter to grease the bottom of a rimmed baking sheet.
Cut the buns in half horizontally. Place the bottom half of the buns on the baking sheet cut side up.
In a small bowl, mix together the Dijon mustard and mayonnaise.
Spread the Dijon and mayonnaise mixture across the bottom half of the slider rolls. Top with a layer of ham (use about half of the ham), then a layer of Swiss cheese (use all of the cheese), and then a layer of the remaining ham. Place the top half of the buns cut side down on top of the sliders, and press down slightly.
In a small bowl, mix together the melted butter, garlic cloves, poppy seeds, and dried parsley. Brush the tops with the melted butter mixture.
Bake uncovered in the preheated oven for 12 - 15 minutes, or until the sliders are warmed through and the cheese is melted.