Place the mozzarella atop 1 bread slice. Sprinkle with salt and pepper. Add the tomato slices and then the basil leaves. Top with the second bread slice. Brush both sides of the sandwich with the oil.
Heat a grill pan over medium-low heat. Grill the sandwich until the bread is golden brown and the cheese melts, pressing down with a metal spatula or grill press, about 4 minutes per side.