Break the lasagne noodles into pieces (3-4 for each noodle).
Bring a large pot of salted water to a boil. Add the broken lasagne noodles and cook, stirring occasionally to keep them from sticking to the bottom. Cook until al dente, just tender. Drain and lightly toss in about 2 tablespoons olive oil.
Cut the tomato into about 1/4 inch thick slices. Cut the mozzarella in about 1/4 inch thick slices too.
Preheat oven to 425˚F. Grease an 8x8 inch baking dish with olive oil. Add half of the cooked lasagne noodles to the bottom of the pan. Arrange the tomato slices, noodles, and mozzarella slices at a semi-upright angle over the bed of lasagne noodles so all the parts are showing- tomato slice, noodle, mozzarella slice, noodle, until the baking dish is filled.
Drizzle with olive oil and season with salt and pepper. Bake in preheated oven until cheese is melted and the tops of the noodles are starting to turn golden, 12-15 minutes.
Sprinkle with basil leaves before serving and drizzle with balsamic reduction if desired.