Preheat oven to 400°F. Pour half of the melted butter onto a large sheet pan, spreading it evenly across the surface.
Arrange 12 slices of bread (4 of each flavor) in an overlapping pattern on the sheet tray. Keep each flavor of bread in its own row to distinguish between the panini varieties. You should have 3 rows of four slices.
Arrange the fillings:
– For Ham and Cheddar Panini: Combine Dijon mustard, honey and mayonnaise in a small bowl and whisk to blend. Spread 1 tablespoon Honey-Dijon mixture on each of the 4 Potato Bread slices; top evenly with sliced ham, cheddar cheese, and bacon.
– For Roast Beef and Asiago Panini: Combine the mayonnaise and rosemary together in a small bowl. Spread 1 tablespoon rosemary mayonnaise on each of the 4 Butter Bread slices; top evenly with roast beef and asiago cheese.
– For Turkey and Provolone Panini: Combine mayonnaise and pesto, stirring well. Spread 1 tablespoon pesto mayonnaise mixture on each of the 4 Whole Wheat Potato Bread slices; top evenly with turkey, provolone cheese, and tomato.
Arrange the remaining 12 slices of bread in the same overlapping pattern as before, on top of the fillings. Brush bread with remaining melted butter.
Place a second sheet pan of the same size on top of the sandwiches and press down. Top with a heavy oven-safe skillet to keep pressure on the sandwiches. Bake in this way for 20 minutes or until the fillings have warmed through.
Remove the weighted pan and top sheet pan layer and bake another 20 minutes or until panini are golden brown and cheese is melted.
Remove from oven and carefully flip the sheet pan over onto a large cutting board. Cut panini into squares and serve.