Split the Cuban rolls lengthwise. Spread the cut sides with the softened butter.
Spread 1 tablespoon of yellow mustard inside each roll. Layer each with 2 slices of smoked meatloaf, one-quarter of the ham, 2 slices of Swiss cheese, and one-quarter of the pickle slices.
Heat a large skillet over medium heat. Place two sandwiches in the skillet and press them with a heavy pan or spatula.
Cook for 3 to 4 minutes, pressing occasionally, until the undersides are crisp and golden. Carefully flip and cook for another 3 to 4 minutes, until the cheese is melted and the filling is hot. Repeat with the remaining sandwiches.
Cut the sandwiches in half and serve warm.