Heat panini press. Cut each bread section horizontally, leaving 1 side attached.
To assemble each sandwich, open cut bread; spread bottom with 1 tablespoon mustard. Top with 1 cheese slice, 1/4 ham slices, 2 pickle planks and 1 cheese slice. Press top of cut bread down over filling. Brush outside of bread with about 2 teaspoons butter.
Place 2 sandwiches into press. Close press; cook until golden brown and cheese is melted (6 to 8 minutes). Repeat with remaining sandwiches.
If you don’t have a panini press, heat skillet over medium heat. Place 1 or 2 sandwiches into skillet. Place another skillet on top of sandwiches to flatten them. Cook, turning once, until golden brown and cheese is melted (6 to 8 minutes). Repeat with remaining sandwiches.