Preheat panini press or nonstick skillet to medium-high heat.
Cut ¾ way through rolls, creating a hinge. Lightly butter outside of rolls. Assemble sandwich by adding ham, tomato, cheese, spinach and basil.
Cook in panini press per instructions, until bread is golden brown and cheese is melted. If using skillet, place sandwich in skillet and lay heavy pan on top to press sandwich down. Cook 3-6 minutes, or until light brown. Flip and continue cooking 2 minutes, or until cheese is melted.