Preheat your oven to 350°F. While the oven is preheating, whisk together the ingredients for Dijon mustard dip and set aside.
Slice the rolls in half horizontally to form a top and bottom bun. Evenly spread half of the mustard dip on one or both cut sides of the rolls.
Place half of the sliced ham on the bottom bun, and top with Swiss cheese. Then, place the remaining sliced ham on the Swiss cheese and top with grated gruyere cheese.
Place in the oven for ten minutes in order to start melting the cheese.
Remove the rolls, and place the top bun on the melted cheese. Glaze with ½ of the garlic butter sauce, wrap in parchment paper and aluminum foil and bake for 20 minutes.
Remove the sliders and unwrap to expose the top buns. Return to the oven for five minutes to brown.
Remove from the oven, glaze with remaining butter sauce, slice and serve hot.