In a bowl, combine mayonnaise and yellow mustard at a 5:1 ratio, using more mayo than mustard. Add garlic powder, onion powder, salt, and pepper to taste. Mix well and set aside.
Add minced garlic and butter to a basting pot on the griddle over high heat. Let the butter melt and infuse with the garlic, then reduce the heat to low.
Slice the rolls in half horizontally, keeping the tops and bottoms intact. Layer Black Forest ham and Havarti cheese on the bottom half. Spread the prepared sauce on the inside of the top half.
Pour some garlic butter onto one side of the griddle and place the bottom half of the rolls on top. Add a small squirt of water nearby and cover with a basting dome to help melt the cheese.
On the other side of the griddle, add more garlic butter and place the top half of the rolls cut-side down to toast.
Once the cheese is melted, add arugula on top of the ham and cheese. Place the toasted top half of the rolls onto the bottom half.
Brush the tops with additional garlic butter, sprinkle lightly with salt, then slice, serve, and enjoy.
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