Spread the mustard on the inside of both halves of bread. Spread 2 tablespoons of butter on the inside of the bottom half of the bread.
Layer the Swiss cheese on both halves of bread. Place a layer of ham and then pork on the buttered half, then carefully top with pickles and the top half of bread.
Spread the remaining butter all over the outside of the sandwich, then wrap it in aluminum foil and press down gently. (Cut the sandwich in half and wrap separately if cooking on the stovetop. Leave sandwich unwrapped if using panini press.)
On the Grill:
Heat your grill to high and close the lid. After 15 minutes, lower the heat to medium-high.
Place the wrapped sandwich on the grill, then set a heavy, heat-resistant object like a grill press or cast iron pan on top. Close the lid and grill for about 5 minutes, then flip and repeat.
Remove the sandwich from the grill and unwrap it. Return it to the grill and grill for 2-3 minutes per side, or until crispy and golden brown.
In a Panini Press:
Butter both sides of the panini press and press sandwiches with medium pressure until crisp on both sides, 8-10 minutes.
On the Stovetop/Griddle:
Preheat a large cast iron skillet, or griddle over medium heat.
Place the wrapped sandwich on the skillet/griddle, and use another skillet or heavy object to press it down with as it cooks. Flip and repeat until sandwich is crispy and hot.
Cut the sandwich at an angle into smaller portions and serve while warm.
If you can't find Cuban bread, a french loaf would be an appropriate substitute.