Preheat oven to 450 degrees F (230 degrees C). Place an oven rack about 5 inches from the heat source. Prepare a baking sheet with cooking spray.
Arrange halibut on prepared baking sheet and bake until lightly browned, 4 to 6 minutes. Flip fillets, season with salt and black pepper, and continue cooking until flesh is opaque, 1 to 2 minutes more.
Top each fillet with a mozzarella cheese slice, a basil leaf, and a tomato slice, respectively; repeat layers.
Return halibut to oven and bake until cheese begins to melt, about 2 minutes.
Whisk balsamic vinegar and olive oil together in a bowl; soon over halibut portions. Garnish with chopped basil to serve.