Preheat oven to 375ºF. Line a large baking sheet with foil. Put ciabatta slices on the foil and coat both sides with cooking spray. Sprinkle with 1/4 teaspoon salt, 1/8 teaspoon pepper and all of the Parmesan. Bake until lightly browned, 5 to 6 minutes.
Arrange tomatoes on a platter or plates with slices overlapping. Scatter on the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Tuck basil leaves in among the slices and crumble goat cheese over the top.
Put vinegar in a small bowl and whisk in oil in a slow trickle until blended and thickened. Drizzle over salad and serve immediately with the ciabatta chips.
Tip: For a more colorful salad, use a combination of red, yellow, and purple heirloom tomatoes.