For extra flavor, grill the onions and add sliced sweet tomatoes (when in season).
Brush each bread slice with a small amount of balsamic vinegar. Arrange 2 slices provolone, 2 slices onion, and 3 to 4 basil leaves on half of bread slices. Sprinkle with pepper, and top with remaining provolone and bread slices.
Melt butter in a cast-iron or nonstick pan over medium-high heat. Add sandwiches to pan, and cook, pressing down with back of spatula, 2 to 3 minutes on each side or until cheese melts and bread is golden brown.